January, thus far a month of cruel cold and heavy snow, dealt the Washington area another punch yesterday, dumping 3 to 8 inches of snow across the region. Forecasters predicted more bad weather today.

The National Weather Service recorded 3.4 inches of new snow yesterday at National Airport, bringing the total snowfall to 10.5 inches since New Year's and creating morning rush-hour headaches for commuters. With 10 days left in the month, this is already the snowiest January since 1966, when 21.3 inches fell, the weather service said. Last year, in comparison, only 4.2 inches of snow fell here in January.

The weather service predicted that today will be messy as well and has issued a winter storm watch. The forecast is for light snow, expected to begin in the late morning, followed by sleet or freezing rain.

Schools in Washington and throughout suburban Maryland and Virginia were closed yesterday, and school officials were waiting until the early hours to decide whether any closings would be necessary today.

Early-morning snow caused numerous accidents yesterday, including a two-car collision on Layhill Road in Montgomery County at 10 a.m. that killed Charles Blackburn, 58, of 2713 Weller Rd., Wheaton, county police said. Police said another motorist, Murray W. Preston, 21, of Sandy Spring, lost control of his car, which skidded across the center lane, striking Blackburn's car and knocking it off the road into a stand of trees. Preston, who suffered a cut lip, was charged with failure to reduce speed to avoid a collision, police said.

The second major snowstorm of the month, which state police said brought up to 8 inches in the northern half of Virginia, also put added strain on government snow-removal budgets. The Virginia Department of Highways and Transportation, for example, said yesterday it has spent about 80 percent of its yearly budget for snow removal in just the last 10 days, and would have to shift money from other accounts.

As snow accumulated through the early morning yesterday, road crews that had been salting major roads were forced to start plowing instead, according to the D.C. Department of Transportation. Icy conditions made travel hazardous in much of the area and forced the closing of sections of Beach Drive in Rock Creek Park early yesterday. By midafternoon, most jurisdictions reported major arteries clear but most secondary roads still slippery.

Ridership appeared heavier than usual at many Metrorail subway stops, especially since maintenance problems idled about six cars during rush hour and created some crowding, a Metro spokesman said. Red Line riders had morning rush-hour delays because of a train breakdown at Van Ness-UDC station and a train with overheating brakes near Judiciary Square.

Federal offices were open yesterday, but employes delayed by weather in the metropolitan area were allowed to arrive late, or take the day off as annual leave or leave without pay, by virtue of an early-morning ruling by the Office of Personnel Management.

The heavy snow also forced cancellation of President Reagan's planned visit yesterday to the Park Heights neighborhood in Baltimore. Reagan was to tour an industrial park in the economically depressed community to promote the concept of "enterprise zones" for creation of new jobs.

Instead, Baltimore city officials were invited to lunch at the White House. Businessmen in Baltimore had been invited to join the president for a sumptuous luncheon of lobster, shrimp, caviar and chocolate mousse, according to a City Hall spokesman, who said the insurance company that paid for the meal had invited the businessmen to lunch today so the food wouldn't be wasted.

In addition, the spokesman said, soft drinks and sandwiches intended for the large contingent of reporters and photographers that planned to accompany the president were distributed instead to poor neighborhoods yesterday.