The nation's governors opened their annual winter conference in Washington yesterday with complaints that federal disaster relief is poorly designed to cope with drought and with the impact of the severe winter.

Gov. James A. Rhodes of Ohio said that federal policies were adequate only when the disaster was a single cataclysmic act, such as a flood. He said the human hardships and the impact on state and local governments of the 1976-77 winter had been "as damaging as a hurricane."

Rhodes said Ohio had been able to qualify only for emergency snow removal assistance. The state has endeavored, so far without success, to obtain federal aid for other needs, including $90 million to help 300,000 poor people pay huge increases in their utility bills.

A similar point about a different disaster was made by California Gov. Edmind G. (Jerry) Brown Jr., who said he had flown to Washington to seek drought relief for his hardpressed satte.

Brown said that water rationing was a possibility this year in California and that there is a need for disaster relief loans and for pumping and drilling assistance from the Army Corps of Engineers to develop new wells. Agriculture production and livestock are threatened by the continuing drought, Brown warned, but he said it is difficult to qualify for disaster relief assistance under existing federal regulations.

"A cow doesn't get fattened up, because of lack of grass on the ground," Brown said. "That doesn't qualify as a disaster, but it may put the cattleman into bankruptcy."

Since his election in 1974, Brown has been scornful of the effectiveness of the National Governors' Conference and has avoided previous meetings, he said he had changed his mind because of the severity of the drought and because of Carter's expressed interest in the governors.

"Given the fact we have a former governor as President, this may make the Governor's Conference a more effective vehicle for public policy," Brown said.

Earlier, a subcommittee chaired by Gov. Richard D. Lamm of Colorado agreed to ask President Carter for a series of changes in administration of drought relief policies. Among other things, the governors want a single federal official designated as a liaison. They also want regional administration of federal anti-drought policies.

Jack Watson, the White House Cabinet secretary, has been designated to administer drought policies. Watson said that so much of his time has been taken up with weather-related calamities that he has been called the "secretary for pestilence, drought and other natural disasters."

President Carter will discuss the drought when he meets with the governors this afternoon at the White House. Watson seemed to be warning the governors in advance that the federal government has more sympathy than money to deal with weather-related problems.

"I'll be frank to say resources are not limitless," Watson said.

Watson urged the governor to make the President's commitment to "Cabinet government" work by taking problems directly to Cabinet officers and their deputies rather than to the President. Watson observed that he was not equipped to be "a case worker" and he said that the attempt at Cabinet government would fail if public officials brought relatively minor problems to the White House.