It probably would be an exaggeration to say that Henry Powers holds President Carter's political fate in the palm of his leathery hand. But not much of an exaggeration.

Powers, proprietor of the Sprague Energy's Co.'s tank farm and refinery here, is New Hampshire's No. 1 wholesaler of middle distillate fuel oil, this state's No. 1 home heating fuel. Next winter, when Carter comes here for the nation's first presidential primary, his fate at the polls may well rest on how much fuel Henry Powers and the 150 heating oil retailers who depend on him can distribute to New Hampshire voters in the cold days leading up to the Feb. 26 primary election.

"If Carter can't come through on heating oil," says Norm D'Amours, the local Democratic congressman, in a comment about as subtle as political talk here ever gets, "he shouldn't even come to New Hampshire next February."

"If Sprague Energy can't get heating oil, this could be a grim winter in New Hampshire," chimes in John Durkin, the state's Democratic senator who keeps dropping hints that he will mount a favorite-son challenge to Carter in the primary.

Durkin says the heating oil problem "is setting the stage for a major catastrophe."

The potential for catastrophe, if there is any, stems largely from a dispute between Henry Powers and his chief supplier, Shell Oil Co. Powers wants Shell to sign a contract guaranteeing him as much fuel as he needs at a specified price. Shell, which says it can use its oil more profitably elsewhere, doesn't want to sign.

Recognizing the political concern over his situation, Powers has adroitly enlisted members of Congress, the governor, and the Carter administration to muscle Shell into delivering the hearing oil.

Shell's basic concern in all this is not politics but plastics. R. N. Hall, Shell's manager of domestic oil supplies, told a congressional committee two weeks agao that Shell wants to get out of the heating oil business in the Northeast because it can make more money turning its crude oil into plastics and petrochemicals in its refineries in the Southwst.

The dispute between Sprague Energy and Shell epitomizes the difficulties facing the New England states as they look ahead to winter.

So far, political and environmental pressures have prevented construction of any big refineries in the region. That means heating oil has to be shipped in from the Caribbean and the Gulf Coast. But refiners there are cutting back on middle distillate sales to New England.

The New England Fuel Institute, an association of heating oil distributors, says reserve stocks are down sharply from last year's levels. And it says most firms have been unable to get a contractual commitment for deliveries of specified volumes at specified prices for the winter.

The problem is particularly acute in New Hampshire, because the state is heavily dependent on heating oil - 73 percent of the homes here heat with oil - and because New Hampshire winters are so severe.

At dawn on an average February day the temperature is 9.9 degrees. If the sky is clear, the thermometer will climb to the high 20s by mid-afternoon before starting to plunge again in the evening.

This kind of weather will greet Carter and everybody else who travels here to compete in 1980's first presidential primary. The prospect of a president campaigning before a frozen electorate has turned the oil problem into a big political issue here.

Even the existence of the problem sparks political debate. While most Democrats - including Gov. Hugh Gallen, the chairman of Carter's reelection drive-agree that heating oil supplies are in jeopardy, Gordon Humphrey, the Republican senator, disagrees.

As Humphrey tells it, the most serious heating oil problem is the scary rhetoric the situation has prompted from his Democratic counterpart, Durkin."He has demagogued this whole, entire issue," Humphrey says.

Even Powers concedes taht "this thing has been politically footballed so much it's disgusting." But Powers doesn't complain much, because he has been one of the chief footballers.

A hardy 47-year-old who started in the oil business as a crewman on an ocean tanker, Powers worked up through the ranks until 1972, when he became president of Sprague, which owns a string of tank farms along the coast from Rhode Island to Maine and a small refinery here.

The refinery, Powers says, is "just a teakettle," producing 13,000 barrels of fuel per day. (The big Caribbean refineries turn out 500,000 barrels daily.)

The Sprague refinery can produce about 26 million gallons of heating oil annually, but this production accounts for less than 40 percent of Sprague's sales. The remaining 60 percent is purchased from outside suppliers. For the past 22 years, Sprague's main supplier has been Shell.

Four years ago, Shell told Powers it was phasing out its Northeast contracts, but it has continued to supply Sprague on a noncontractual basis. Last month, Powers asked Shell for a contractual commitment for next winter but Shell refused.

"I knew I'd have to get aggressive.," Powers said. "I didn't just fall off a turnip truck, you know. I've been in this game a long time."

Somehow, the Shell-Sprague correspondence was leaked to Powers' favorite golf partner, Raymond Brighton, editor of the Portsmouth Herald. The Herald's stories turned Sprague's business dispute into a statewide concern.

Powers then asked the state's congressional delegation for help. Last Thursday, accordingly, Powers sat down with a group of Shell officials for a negotiating session in Durkin's Senate office in Washington, D.C.

Durkin invited other New England officials to attend the session. By sheerest coincidence, all those invited were Democrats. This irked Humphrey, the Republican, so the Shell people and Powers agreed to hold a second negotiating session later that day in Humphrey's office.

This arrangement permitted members from both parties to put out press releases claiming they had helped solve New Hampshire's fuel problem.

Powers also appealed to Gallen for help. "As governor of the state that has the first primary," Powers explained, "Gallen simply has the ear of people who can do things." Gallen placed a call to Carter at Camp David. The governor won't say exactly what transpired, but he says he is confident that Shell will meet New Hampshire's needs.

Legally, the president do much. Although the federal government can order state-by-state allocation of gasoline, it doesn't have that power over heating oil. It can order refiners to prodcue the fuel, but it can't tell them where to ship it.

Shell, nonetheless, seems to have gotten the word. The company said Friday it will see to it that "nobody freezes in New Hampshire."

Henry Powers still isn't satisfied. He notes that Shell's commitment is oral because the company won't sign a heating oil contract. "They're playing Russian roulette" with New Hampshire, Powers said.

"I have an obligation to get adequate fuel for this state. If I don't, people better not come here in February looking for votes." CAPTION: Picture 1, HENRY POWERS . . . "I knew I'd have to get agressive"; Picture 2, Sprague Energy's tank farm and refinery - "just a tea kettle" - produces only 13,000 barrels of fuel per day. Aerial photos of New England Inc.