President and Mrs. Reagan could have held their dinner for the governors outside last night, the weather was so balmy for the Winter Meeting of the National Governors' Association.

And the warmth of the night air extended into the White House state dining room, where the governors and the former governor (as Reagan reminded them) clinked their glasses and toasted to cooperation.

"The challenge before us, especially concerning tax simplification and spending restraint, will require great courage and effort and extraordinary cooperation between us," the president said in his toast.

Even National Governors' Association chairman John Carlin, (D-Kan.), responded, "You have appropriately commented on some of the critical issues, and now is not the time to respond."

Many in the audience knew that meant that last night's tropical breeze could turn into a cold front today, when the governors bring their concerns about cuts in state aid to the White House at a meeting with the president. "There is a sense that we want to do our fair share," said Gov. Madeleine Kunin (D-Vt.) of the proposed budget cuts, "but states like Vermont can't afford having the burden shifted toward us . . . I think there'll be some serious questions asked that you can't ask tonight. I'll be asking."

President Reagan knows many of these governors will be asking. "Having been a governor," Reagan said, as his wife Nancy tugged him by the hand toward the East Room for the entertainment, "I know they'll be capable of asking some penetrating questions."

In his toast, Reagan warned that the decisions that lie ahead will not be easy: "Today, the people no longer look to Washington as an emerald city with magic solutions to every problem. I've been here going on five years, and I can tell you it's more like the Twilight Zone than the Land of Oz."

On the farm issue, Reagan said Saturday in his radio address that the White House will help but that "American taxpayers must not be asked to bail out every farmer hopelessly in debt."

Said Nebraska Gov. Robert Kerrey, a Democrat, "We're not asking for a bail-out. I agree with him. He's answering the question we're not asking. So let's talk about what's happened to agriculture in the last four years. Government's pounded it into the ground with deficit spending . . . We've got 15 percent of our producers who may not make it this year. We have more foreclosures than during the Depression. We're not asking for a bail-out . . . We're asking for the government to assume their share of the responsibility and they're not."

Arkansas Gov. Bill Clinton (D) said that states "are prepared to take some cuts -- as long as they're balanced . . . To continue these huge increases in defense spending and then cut the domestic budget -- it can't be justified."

Clinton echoed Kerrey's words about farmers, noting that "we're in the most drastic change in the whole structure of rural life since the Depression . . . It's not just another bad year for farmers. The whole structure of agriculture is going to change."

Not only the governors were talking about farmers last night. In the early evening, a group of business-suited state legislators -- in town for their conference -- tried unsuccessfully to deliver a letter to President Reagan asking him to meet with them to discuss the farm situation. "They said they didn't accept deliveries on Sunday," said Tom Vickers, a state senator from Nebraska, as he stood outside a White House gate. "We'll be back to put it in the mail room at 7 a.m. We're serious about this. We want to be able to articulate to the president and the lawmakers that a terrible black cloud is looming over recovery."

Of course, not all the governors were protesting cuts in state aid. "I don't see how we can give him a hard time and still want to cut the deficit," said Republican Gov. James Thompson of Illinois. "Governors are more mature about this. We have to do our share."

Absent from the ranks of dining governors last night was New York's Mario Cuomo (D), who sent his regrets yesterday evening, according to White House social secretary Gahl Burt.

However, Kerrey, who was apparently expected by the White House to arrive alone, brought a date -- Cynthia Giordano, a Washington attorney with Linowes & Blocher. White House staffers were a bit startled by the new guest but quickly took care of the situation with a little shuffling of chairs and place cards.

For the entertainment, singer Lee Greenwood sang his hit country single "It Should Have Been Love by Now," which inspired Virginia's Democratic Gov. Charles Robb and his wife, Lynda, to hold hands. He also sang the song that has become the unofficial anthem of the Reagan administration, "God Bless the U.S.A." "I just wanted to write a song about how freedom is such a fragile thing," Greenwood said of the song, which may win him a Grammy tomorrow for best country male vocal. Last night, he saved it for the finale.

After the entertainment, President Reagan said about Greenwood, "There was a lot of speculation about why the campaign came out the way it did -- and now you know. Because we had him on our side."

The Reagans joined the governors and their spouses in after-dinner dancing. Arkansas' Clinton and his wife Hillary danced through several songs, belying what the youngest Democratic governor -- at 38 -- had to say about his state of mind. "I feel like I'm the oldest man in America my age," said Clinton, who's been governor since he was 32. "I've been in it so long. I'm grayer than half the people here. But I love it."

And outside on the front veranda of the White House, where guests had essentially moved the party outside, chatting and sipping champagne, Republican Michael Castle of Delaware, who's been governor 41 days, remembered his Georgetown Law School days. "I drove past the White House for three years," he said fondly.

Now he's a guest.