Bitter cold weather, honed by high winds, hit the Washington area yesterday, with some snow expected to fall here today, as many areas of the nation were battered by elements of the new winter.

Record cold temperatures already had blanketed much of the country earlier in the week with 15 to 20 inches of snow reported in some eastern states. Snow emergencies were in effect in a number of cities, most notably Cleveland, which had 7 inches of snow on the ground by yesterday with 3 to 6 more inches in the forecast.

Washington area temperatures are expected to dip into the teens and low 20s early today. There is a 70 per cent chance of precipitation with a "good chance" of some snow by late afternoon, the forecaster said. Although the snow - if it comes - is expected to stop falling by late evening, extremely cold temperatures are predicted through the weekend. The high today is expected to be in the mid 30s.

Although Washington and Virginia were not hit by snow yesterday, parts of Maryland were. Garrett County schools in western Maryland were closed because of snow-covered roads.

In Baltimore County, about 4,400 homes in scattered areas were without power early in the day as wind felled power lines and trees, which in turn crashed into utility poles. Winds gusted up to 50 miles an hour in parts of the state.

In Virginia, snow was forecast in many areas for Thursday and temperatures dropped as low as 4 degrees - in Bristol. The wind-chill factor, influenced by 15-mile-an-hour winds, was recorded at -1 degree in Richmond early yesterday.

The forecast for much of the state Thursday read: "Bitter cold, snow likely."

Nationally, people in the Midwest, Rocky Mountains and the Northeast began bracing for another bout with snow and the wintry conditions that plagued most of the nation a year ago.

Even though winter still is two weeks away - by the calendar - schools throughout Pennsylvania were closed yesterday as 6-foot-high snow drifts blocked roads. In Indiana, travelers were housed in National Guard armories as highways became impassable.

Parts of the Mississippi River were frozen bank to bank and shipping on the northern Great Lakes was hampered sharply. In Cut Bank, Mont., the day's lowest temperature - minus 20 degrees - was recorded with a wind chill factor reaching - 80 degrees.

Although much of the low pressure center that had dropped 15 inches of snow on Rochester, N.Y.; 18 inches in Brunswick, Maine and 21 inches on Brdford, Pa., had headed out to the Altantic by yesterday afternoon, another cold front moving out of the Rockies promised continued cold weather for the Midwest and East.

The cold weather also extended south, however. Asheville, N.C., reported temperatures as low as 5 degrees yesterday, lowest ever for the month of December. Readings dropped to near freezing in parts of Florida, but there was no reported threat yet to the fruit crop.

Although Washington area power companies reported no problems in supplying customers with the extra power they demanded, the weather forced the Tennessee Valley Authority, which services 10 million customers, into drastic action.

With nearly one-third of its generating systems shut down for repairs and winter preparations this week, the TVA was forced to cut its voltage by 5 per cent Tuesday and asked customers to reduce their use of electricity. In the meantime, the TVA purchased about 2 million kilowatts of power from utilities in Pennsylvania, New Jersey, Illinois and Missouri.

Relief did not appear to be in the immediate offing, with the National Weather Service forecasting blizzard conditions in North Dakota and continued storms throughout the Midwest.

"This storm has the potential to be a real troublemaker for all travelers and people with outdoor activities by late tonight (Wednesday) and Thursday," a spokesman said.

Typical temperature and weather conditions included: Cincinnati - (2, snow); Cleveland (7, snow) Indianapolis (-7, snow); pittsburgh (9, snow) and Toronto (12, snow).