When the Senate Public Works Committee began to chop up the Economic Development Administration (EDA) and Appalachian Regional Commission (ARC) four months ago, Sen. Jennings Randolph (D-W. Va.), who proudly sired the two ventures during the free-spending days of the Great Society, couldhardly hold back the tears.

President Reagan wanted to kill the programs, and it looked as though the committee Rnadolph had headed until the Republicans took control of the Senate earlier this year would go along.

But last week Randolph was all smiles.

Slimmed down, maybe even a little emaciated, the once well-padded programs have survived.

"They live . . . and I'm a happy man," Randolph beamed after House-Senate conferees locked in $290 millionfor the EDA and $215 million for the Appalachian program during an evening of hard bargaining. Randolph and his Democratic allies fromthe House were playing the game of "damage control" like the old pros that they are.

By almost any yardstick, Reagan and his relentless budget director, David A. Stockman, already have won a historic victory in reversing, or at least sharply modifying, the half-century trend of ever-growing government and ever-expanding social services.

Out of more than $35 billion in projected savings for next year, a little less than 10 percent of the total budget, conferees on the huge budget "rdconciliation" bill have already nailed down about $33 billion in program cuts, and expect to hit their target by the time the job is completed early this week, according to House Budge Committee leaders.

Even before the start of the huge conference, involving more than 250 lawmakers divided into 58 "mini-conferences," Reagan had won most of what he wanted in roughly similar versions of the legislation passed separately by the House and Senate. This included an emphasis on many big open-ended entitlement programs that provide benefits without regard to costs.

But, for all their spectacular budget losses to the Reagan-Stockman team, the Democrats have managed, at least in some cases, to keep money flowing into threatened programs, their basic structures preserved for another day when the budget-cutting ardor may have waned on Capitol Hill.

If a favority program such as the Eda survives this season, it will be alive in future years when, perhaps, the federal budget will grow again. The Democrats also succeeded in ridding the legislation of at least one major extraneous rider, which would have curtailed housing assistance to cities such as New York and Washington that practice rent control.

For some few programs that have vocal or politically sensitive constituencies, such as the arts and humanities endowments, loans to college students and the Export-Import Bank, which serves exporting industries and their workers, Congress is providing more money than Reagan wanted.

For the politically popular program of government-subsidized student loans, which helps the middle class as well as the poor, House-Senate conferees agreed to a substantially smaller cut than Reagan proposed.

It was even less of a cut than either of the two chambers had approved in their separate reconciliation bills. And, rather than imposing a means test for all loans, as the administration wanted, the conferees agreed to provide loans as a matter of right to students with family incomes of up to $30,000.

Moreover, some major education, health and social service programs, as well as smaller ones, that Reagan wanted to submerge into block grants to the states, an action which critics said might seal their doom, are expected to be preserved as separate programs or as earmarked segments of new block grants.

Examples range from the huge program to help school districts educate pool children to the smaller program of adoption and foster-care services. Community action programs, which grew out of the old war on poverty, are to be preserved to the extent that the National Community Action Foundation proclaimed that "the administration's effort to arbitrarily lump together all social services with no specific commitment to the poor has been given a major setback."

Similarly, the administration would have submerged youth jobs programs intothe general employment program, but Congrss will keep them operating separately, although at a reduced funding level.

In some areas, Reagan is likely to get the dollar cutbacks he wants, but without the structural changes that were even more important to the administration in terms of containing costs in the future.

An example is Medicaid, where the conferees, at least as of Friday, appeared likely to give him his $1 billion in savings without the "cap" on cost growth for which the administration has been fighting.

In a few other areas, such as the EDA, which helps finance industrial parks and other community-development ventures, both dollars and structure have been preserved, to some extent.

Even the Legal Services Corp., whose litigation on behalf of the poor has been anathema to many conservatives, appears likely to survive at a reduced level of operations. Another survivor is the National Consumer Cooperative Bank. Amtrak also is considered likely to keep operating nationwide, although with less service.

Finally, even though the conferees have agreed to eliminate the $122-a-month minimum Social Security benefit for current as well as future retirees, there has been such a political backfire that Republican as well as Democratic leaders are now talking about legislation later to ameliorate the impact.

But these salvage operations have been offset partially by cases in which Congress has shown more zeal for retrenchment than has Reagan. From food stamps, the conferees agreed to cut about $200 million more than Reagan proposed, althought he final figure is less than the Senate originally voted.

One reason the Democrats have been able to score some damage-control points in conference is that legislative conferences are tailor-made for the kind of negotiating and horse-trading skills that Democratic veterans like Randolph and House Public Works Chairman James J. Howard (D-N.J.) have honed over the years.

On some critical issues, a mix of Democrats and moderate Republicans can often make the difference in a conference vote. Perhaps more important, members are voting on specific spending cuts, not the overall Reagan program, the whole of which has always been more popular than the sum of its