Congress took its first vote on President Reagan's proposed budget cuts yesterday and the president easily won as the Senate Agriculture Committee agreed 14 to 2 to skip a scheduled April 1 increase in dairy price supports.

This change in the law would save the Treasury just $147 million this year, but it was a significant symbolic victory for Reagan nevertheless. The committee vote was a defeat for an interest group that has traditionally enjoyed remarkable political success in Congress -- and has been remarkably generous in contributions to members.

The White House had worked hard to win this first test of its policies, and now hopes for a speedy and decisive final Senate vote on the floor. But the legislation eliminating the April 1 adjustment in dairy price supports will also have to clear the Democratic House this month to become law, and the prospects for favorable House action are problematical at best.

Indeed, the fact that the measure must still negotiate a hazardous course through the House Agriculture Committee and the full House probably contributed to the size of Reagan's victory in the Senate committee yesterday. Important segments, of the powerful dairy lobby decided not to try to fight the administration in the Republican Senate. The absence of heavy lobbying and the unusual presence of seven television cameras in the Agriculture Committee's modest meeting room to record the day's decision together might have induced some senators who might otherwise have voted no to go along with the president.

The television cameras don't usually appear in Room 323 of the Russell Senate Office Building where Agriculture meets. It is a pre-TV-era hearing room, with a long narrow table in the middle of the room instead of a raised platform for the senators, Phil Jones of CBS reminded Democratic members before yesterday's session began that they would have to lean back when they weren't speaking so that whoever was speaking would be visible to the camera. This resulted in a lot of Democrats leaning far forward when they had something to say.

A popular subject for discussion at yesterday's meeting from the voters. Sen. Paula Hawkins (R-Fla.) said she'd been reminded of it by a Washington cab driver who told her to support the president's program. Sen. Edward Zorinsky (D-Neb.), leaning far forward, called yesterday's vote "a litmus test" of senators' determination to cut the budget. He then read a letter from a blind piano tuner in Lincoln, Neb., urging support for the budget cuts, a letter Zorinsky said was typical of the mail he was getting.

Many members of the committee were clearly uncomfortable about casting a vote that seemed to go against the interests of dairy farmers. Chairman Jesse Helms (R-N.C.) introduced the session as a meeting on "one of the most effective agricultural programs we have, the dairy program."

Like many other committee members, Helms has received substantial political contributions from the big dairy cooperatives -- $10,500 in 1980, $8,000 from the co-ops that lobbied against yesterday's bill. In all, the three principal political action committees of the dairy farmers gave $146,400 to committee members since 1976, according to figures compiled by Common Cause.

The discomfort was too great for Sens. Patrick Leahy (D-Vt.) and Mark Andrews (R-N.D.). Leahy, representing a dairy state and receiving $27,000 in dairy PAC contributions since 1978, argued that it was unfair to pick on dairy farmers separately. Andrews agreed.

But other farm state stalwarts -- all Republicans apparently susceptible to White House lobbying -- went along.Among them were Rudy Boschwitz (Minn.), Roger Jepsen (iowa) and Bob Dole (Kans.), who voted by proxy from a hospital bed.

In an effort to sweeten the pill they were slipping to dairy farmers, several members of the committee pressed yesterday for an amendment to the bill postponing the April 1 price support increase, which will will rise from $13.10 to $14 a hundreweight if this bill is not enacted. Sen. John Melcher (D-Mont.) proposed the amendment, which would have banned all imports of casein, an all-protein derivative of milk. Cheap casein imports displace potential sales of American powdered milk, Melcher argued, thus contributing to the growing mountain of American surpluses that is costing the Treasury so much -- perhaps $2 billion this year.

The International Trade Commission concluded unanimously in 1979 that casein imports had no significant impact on powdered milk sales, but Melcher and like-minded senators ignored that finding. Melcher's amendment nearly made it, failing on an 8-to-8 tie vote.

Full Senate action on the bill is expected soon, and passage seems likely. Then the pressure will be on in the House, where pro-dairy members will only have to stall the bill until April 1 frustrate this first budget-cutting initiative by the new administration.