It makes a somber postcard, black from the rain of coal dust and white from the recent snow, and you know it had to be a terrible explosion.

It started where they were mining, about 800 feet under the mountain, igniting the volatile dust into an infernal force that rushed to the surface like a projectile from the barrel of a cannon.

All seven miners, including three Hamilton brothers who ran the operation, were killed in the Jan. 20 eruption at the RFH Coal Co. Bodies were burned and twisted beyond recognition. The conveyor belt was a tangle of metal. Trees and land outside the mine turned black from the dust spray.

This disaster and a rash of other mine accidents that killed at least 33 Appalachian miners in December and January have touched off a flurry of state and federal investigations of the kind that traditionally follow mining tragedies.

But there is a difference this time.

The federal inspection force, built up gradually after major disasters in 1968, 1970 and 1976, is reeling from Reagan administration budget cuts and policy changes. Critics draw a direct link between these changes and more deaths and accidents, fewer inspections and violation notices in the last year.

President Reagan's proposed 1983 budget was to have cut $7 million more from mine safety enforcement. But in an unusual move, the White House last week amended the figures upward before the ink on the budget was dry.

Even that, however, won't return mine safety spending to its pre-Reagan levels and, in keeping with its promise to cut the tangle of government rules, the administration is pursuing a regulatory reorganization that skeptics view with alarm.

But to some inspectors in the heart of the nation's coalfield, the contemplated reorganization would simply formalize a policy that is already understood.

"We've lost direction. The morale of the inspector is destroyed," said Hugh Smith, a federal mine inspector based at nearby Pikeville. "It has never been put in writing that we shouldn't enforce the law, but our people know there's a change in attitude in Washington. You only have to watch the 6 o'clock news to know this."

A three-month strike by the United Mine Workers notwithstanding, there were 153 fatalities in 1981, compared with 133 the year before. Through Thursday, there have been 26 fatalities in 1982, compared with 15 during the same period last year.

The Department of Labor's Mine Safety and Health Administration (MSHA) last year assessed 27 percent fewer civil penalties; its inspectors issued 16 percent fewer violation notices and 9 percent fewer mine-closure orders in fiscal 1981 than a year earlier.

The case of the RFH mine here in Floyd County puts still another light on the picture. Evidence gathered by federal investigators suggests that blatant safety violations were occurring at RFH when it blew up. But on paper, if official inspection reports are to be believed, the RFH mine was a paragon of safety.

During four inspections in 1981, MSHA inspectors gave RFH a clean bill. The mandatory inspections produced only one safety violation notice. Similar spotless records are turning up at other small mines. "The number of violation-free mines last year would shock you," said one official. MSHA is conducting an internal study to determine why historically dangerous mines are suddenly showing up clean.

Although Reagan altered his 1983 budget to lift the freeze on hiring coal mine inspectors, the administration is proceeding on other fronts with policies that appear to have had a severe effect on MSHA morale, both here and in Washington.

Some examples:

* MSHA chief Ford B. Ford, aiming for a new era of "cooperation" with mine operators, has shifted more power and duties to MSHA's district managers. Among these will be a procedure, scheduled to take effect in April, that will allow operators to meet privately with the managers to discuss the validity of violation notices issued against them.

* Since last fall, MSHA has applied rigid new civil service performance standards to its inspectors, who complain that the result is work schedules that force more cursory, speeded-up inspections and fewer surprise spot inspections in the mines.

* The hiring freeze has sharply cut the size of the inspection force. For example, the Pikeville district of MSHA, covering a major coalfield, is 44 inspectors below its 1978 level. In MSHA's Prestonsburg office, with clerical help laid off by budget cuts, key supervisors have been relegated to handling paperwork. Nationally, the agency has about 850 inspectors on duty, less than half the 2,000 that an internal MSHA study says are needed to provide full coverage of the mines.

* The administration has not taken a formal position, but congressional sources expect it will line up in support of a package of amendments drafted by the American Mining Congress and introduced by Sen. Orrin G. Hatch (R-Utah) to substantially water down the tough 1977 mine safety law.

* Fearing layoffs or loss of jobs, many younger inspectors, almost all miners before joining federal service, are said to be nervous about penalizing mine operators from whom they soon may have to seek employment. "It's hard to regulate an industry you might have to ask for a job next week," said a furloughed MSHA employe in eastern Kentucky.

Hugh Smith, president of the Pikeville local of the American Federation of Government Employes, added: "We're going back to the way things were in this industry before the Farmington W.Va.disaster in 1968. We've come too far to turn back now . . . . We can't let the budget be balanced on the blood of Kentucky coal miners."

The trends were too much for Ralph Blackburn of Robinson Creek. He resigned as an MSHA inspector a couple months ago to return to a job in the mines. "These changes have affected morale badly," he said. "I felt I wasn't being backed up. I was rushed and I had to take short cuts on inspections. I was afraid I would get someone hurt at my mines. I didn't want that on my conscience, so I quit."

James Boyd, a UMW safety official based in Pikeville, put it this way: "Put yourself in those inspectors' shoes. Their attitude is very poor. Their morale is plain gone. They may be looking for a job next week from the same guy they're inspecting. They're just not spending the time in the mines that they used to and we're getting more complaints about safety from our men at the local mine sites."

In an opinion issued last month, affirming a $200,000 penalty settlement against the owners of the Scotia Coal Co. mine in Kentucky where explosions killed 26 men in 1976, a federal administrative law judge lashed out at the mine-safety budget cuts from another angle.

Joseph B. Kennedy, a judge with the independent Mine Safety and Health Review Commission, wrote that budget cuts have seriously impaired the morale of inspectors and judges. "In the face of the rising rate of institutional manslaughter," Kennedy said, "the calls for further deregulation and relaxation of the enforcement effort seem unreal, if not morally irresponsible."

Some MSHA career officials in Washington acknowledge the validity of these allegations. Said one: "When our people hear what the president says about overregulation, about bureaucrats and so on, it affects their morale. With the budget cuts, many got furlough notices around Christmas and this has been a big psychological factor."

Inspected or not, the mines continue to run at a merry pace in this part of the mountains. The pressure for production is intense. Loaded coal trucks constantly lumber along the roads. The signs of coal prosperity are everywhere: new homes sprouting on hillsides, new retail outlets, a Prestonsburg store that advertises designer apparel.

One thing does not change.

Coal operators, historically resistant to government oversight, continue to assail MSHA inspections as an example of the overregulation the Reagan administration has promised to abate. In the wake of a grim December and January, some in the industry are calling on regulators to punish miners, rather than operators, for safety infractions.

That line emerged again last week in Hazard, where an investigative commission appointed by Gov. John Y. Brown met to hear miners and mine operators testify on a type of explosive technique common in use here, but banned as too dangerous in most states.

The Hamilton brothers were using this technique, called shooting from the solid, when their RFH mine exploded. At another mine not far from here, the Adkins Coal Co. at Topmost, eight miners died in a similar explosion in December.

After those disasters, the state tightened its rules for this type of blasting. The industry, however, argues that Kentucky, the country's leading coal producer, is inviting economic suicide if the rules are tightened more. Operators at the Hazard hearing claimed that the cost of mechanized equipment to cut out the coal, rather than blast it out, would bankrupt most small operators.

The UMW's Boyd, a member of the governor's commission, couldn't resist when one witness, cutting-machine manufacturer Thomas Pruitt of Grundy, Va., testified that mechanization would vastly reduce explosives costs and save the companies money in the long run.

"What's the difference between the price of a Mercedes and one of your machines?" Boyd asked with a touch of wryness.

"Not a heckuva lot," Pruitt answered.