The nation's coal strike has prompted the White House to begin planning for a remote but not thinkable possibility - a spate of widespread power blackouts is states that are heavily dependent on coal for the generation of electricity.

The planning is under the direction of Greg Schneiders, President Carter's assistant for special projects who is also in charge of revamping the federal government's disaster prepardedness agencies.

Working with the Department of Energy, the Federal Diaster Assistance Administration and other agencies, Schneiders is attempting to answer a question that was not even asked before the coal strike:

What does the federal government do if the lights start to flicker and go out across a whole state or region?

The answer is likely to be that the federal response to a widespread and prolonged blackout would not be much different than the federal response to any large-scale disaster.

There could be serious law enforcement problems and a need to mobilize federal agencies to deal with them. There clearly would be a need for federal transportation facilities to move people and supplies into the affected area.

Right now, according to Schneiders, the planning is focused on determining what federal facilities - for example, emergency power generators - are available, and developing a system to move available equipment to wherever it is needed.

The White House is also seeking to devise a better communications system between the federal government and the states so that a governor, confronted with a large-scale blackout, would not have to find his way through a maze of federal agencies before getting help.

Neither Schneiders nor other officials involved in the planning expect to be faced with widespread blackouts. For that to happen, according to Barry Yaffe of the energy department, the coal strike "would have to go on for months."

To make such an eventuality even more remote, the Energy Department is monitoring the movement of coal and electricity into the hardest hit states in the Midwest and East. At least 10 states now have power curtailment plans in effect, with the result, according to Yaffe, that the rate of decline in cola stockpiles has slowed.

While officials are optimistic that serious blackouts will not occur, the strike has forced the federal government to consider, for the first time, how it should deal with such a situation. Even if the strike were settled tommorrow, one of them said, "before we're done we should have put together contingency plans that might be useful."

In this and in other attempts to plan for dealing with the effects of the coal strike, administration officials are attempting to keep an extremely low profile. They stress that dealing with the strike's effects is primarily a state and local function and they fear raising expectations among state and local officials that massive amounts of federal assistance are being readied for delivery upon presidential order.

"I do not expect any special presidential action," one aide said.