In ceremonies laden with symbolism, jubilant Democrats celebrated their return to power here today with the inauguration of Mark White, a Houston lawyer and former state attorney general, as the 42nd governor of Texas.

White, who defeated Republican incumbent Bill Clements in November, took the oath of office standing coatless in a hard, cold rain on the steps of the Capitol, officially ending the first Republican administration in Texas in more than a century. White was the last of 36 governors to be sworn in around the country this month.

"The people's interest will have a fresh start in my administration," said White, 42, a conservative who campaigned on populist themes. "There will be new faces and new ideas as a new generation of Texans prepares to take over the reins of government."

And then, in an event meant to be reminiscent of the inauguration of President Andrew Jackson in 1829, White walked immediately to the governor's mansion several blocks away, cut away a freshly installed chain locking the gates to the grounds and opened the doors to the residence to hundreds of soaked supporters.

The ceremonies today and Monday were as much a tribute to the Democratic Party as to White, who rode into office on an unprecedented outpouring of voters. Stunned and angry over Clements' election in 1978 and President Reagan's big victory here in 1980, normally divided Texas Democrats united behind Sen. Lloyd Bentsen (D-Tex.), White and Lt. Gov. William P. Hobby to stage the most impressive campaign in memory.

The November elections produced a Democratic sweep and brought into office in Austin a new slate of progressive Democrats, who were sworn in earlier this month. They staged their own symbolic ceremony Monday night in the Capitol rotunda by taking an "oath of open office" from White in which they pledged openness in government.

These and other events were spiced with considerable public comment about the 1984 elections and the role Texas Democrats will play in trying to defeat Reagan, if he seeks reelection. Hobby, normally a somewhat passive politician, called the 1982 defeat of Clements the first of a one-two punch.

"That next punch will come two years from now, when we're going to return the nation to democracy," he said.

But the Democrats' dreams of repeating their 1982 triumphs now will depend in part on how well the diverse cast of characters now in power handles the problems at hand.

Already there are signs of strain in the Democratic alliance. White faces a potentially embarrassing struggle with some members of his party in the Texas Senate over whether to recall more than 100 appointments Clements made after his defeat. A showdown could come Wednesday, with reports of compromise in the air today.

Although he has pleased the liberal wing of his party, White faces continual scrutiny.

"The administration of Mark White is going to be a great administration not just because Mark White will be a good governor, but because the rest of us are going to be there to remind Mark who brung him to the dance," new state Treasurer Ann Richards told a labor luncheon Monday.

White even has a challenger for 1986. Democratic state Comptroller Bob Bullock, a longtime adversary of White, said earlier this month he intended to run for the Democratic gubernatorial nomination in four years.

White also must reconcile various promises he made during the campaign with a revenue forecast that is suddenly pessimistic. In attracting populist support last fall White promised a sharp increase in teacher salaries, reform of the public utilities commission, better roads and transit systems and an expanded prison system, which is under federal court order to reduce overcrowding.

White said he could do that without raising taxes, but last week Bullock announced that estimated revenues during the next biennium will fall $1.5 billion short of earlier projections. That will require cuts in the already tight budget proposed by the Legislative Budget Bureau or increased taxes.

White also must grapple with the recession's impact on Texas, where the unemployment rate is 8 percent.

In his inaugural address, White chose not to dwell on the recession, focusing instead on Texas as "the state of the future," a state "on the edge of greatness."

But Hobby brought the ceremonies into more humble focus in a state facing future water shortages. Speaking to an audience huddled under umbrellas and taking shelter beneath tree limbs on the Capitol grounds, Hobby recited a poem by a former state senator, which ends with this line:

"Not one inauguration's worth a good, slow, two-inch rain."