A new round of heavy rains ushered in the New Year through much of the soggy South, flooding some streets in Mobile, Ala., and forcing more evacuations in Louisiana, where rivers were still rising.

Rain fell across much of Louisiana, but officials said the worst was well to the south of areas where flooding last week forced evacuation of nearly 10,000 people and caused damage estimated at more than $50 million.

But water was still rising in the Ouachita River at Monroe in the northeast and yesterday was measured at 6.4 feet above flood stage of 40 feet, the National Weather Service said.

President Reagan will stop in Monroe today to inspect the flood damage, White House aides said.

Deputy press secretary Larry Speakes said Reagan would visit Monroe for about an hour while en route back to Washington from a six-day western vacation.

Meteorologist Eric Meindl said the Ouachita River was expected to crest "up to 48 feet on the 5th or 6th" of the month.

In southwestern Calcasieu Parish (county), civil defense director Tom McCool said about 350 people had been flooded out of their homes Friday and yesterday, but the worst was over--barring any new major downpours.

Joseph V. Colson, assistant secretary of the Louisiana Office of Emergency Preparedness, said it would be two to 2 1/2 months before some houses could be reoccupied.

Louisiana National Guard Maj. Gen. A.M. Stroud said 150 guardsmen had been activated for flood duty.

Mobile, Ala., on the Gulf Coast, received more than three inches of rain Friday and yesterday.

Charles Kendrick, police radio-communications officer, said several streets were flooded, but the water was running off by midday.

Flash-flood watches remained in effect throughout Saturday night for Mobile and Baldwin counties.

In Mississippi, rain fell across central and southern areas, but no significant amounts fell in the flooded Delta.

John Davis, an Army Corps of Engineers spokesman in Vicksburg, estimated that 1.2 million acres in the South Delta area were under water, most of it agricultural flatland.

In the northeastern part of the state near Columbus, the Tombigbee River was falling and cleanup operations had started. The Red Cross said no damage assessment had been made yet.

In Texas, a winter storm dumped snow and ice in the Panhandle and South Plains while generating cold rain and drizzle all along the Texas-Louisiana border. The storm earlier left up to a foot of snow in the western reaches of Texas.

"It's just generally rotten weather," said Bob Neely, spokesman for the state Department of Highways and Public Transportation, which was monitoring the increasingly dangerous driving conditions in West Texas.

Neely said travel was "extremely hazardous" in the San Angelo area because of icy bridges and overpasses.

A fisherman whose two companions died after their boat sank in 10 feet of water in Galveston Bay was rescued yesterday after clinging to the boat's mast through a night of gale-force winds, rain and 40-degree temperatures.