Jane Byrne greeted an old political ally -- a raging winter snowstorm -- here today, and the embattled mayor proved again that she knows how to get a boost out of a blizzard.

The Byrne administration won unstinting praise from the media, and even grudging plaudits from opposing politicians, after city crews successfully cleared away a foot-thick blanket of snow dropped by a driving storm that blasted through the city Tuesday.

In spite of panicky predictions from radio and television news shows, rush hour commuters today found express-ways just about clear and trains and buses running just about on time. While suburbs all over the place closed their schools, Chicago's were open.

It all made a striking contrast to Chicago's last big snow. That came two years ago, when Byrne was waging a scrappy underdog campaign against incumbent mayor Michael Bilandic.

Bilandic, hit with two big storms 12 days apart, struggled mightily but could not get the streets cleared. Byrne charged that his performance besmirched Chicago's reputation as "the city that works." Politicians of all factions here agree that the snow was an essential factor in Byrne's victory.

After Byrne took over in March 1979, she made snow preparation a top priority. She set up "Snow Command," a city hall office that looks like Pentagon war room. Field commanders responsible for deploying nine divisions of plows and trucks issue their orders amid blinking and chattering computers, teletypes and $40,000 worth of weather radar equipment.

"Snow Command" faced its first serious challenge early Tuesday, when two storm centers converged on Chicago. Snow fell steadily all day, and 40 mph winds whipped great frozen clouds of it across the highways, covering roads as soon as they were plowed.

John Donovan, the city's streets and sanitation commissioner and the director of "Snow Command," said today his team stayed on the job for 30 hours straight to make sure that Byrne's first battle against big snow ended in victory.

Before he went home to sleep, though, Donovan accompanied the mayor to today's City Council session. The two beamed together as alderman after alderman came by the report that "my ward looks real good."

But Chicago's politicians know how to condition their praise of an adversary, and many of those who congratulated the mayor today felt obliged to note that Tuesday's snow was smaller than the accumulation that helped bury Bilandic two years ago.

"It appears that the city did a reasonably good job," said Alderman Martin J. Oberman, an independent who fights both Byrne and the various factions opposing her. "But this was only 10 inches. That's not all that much for Chicago."

Even conditioned praise must sound sweet to Byrne these days. Her support of Sen. Edward M. Kennedy (D-Mass.) in last year's Democratic president primary turned into a calamity for both Byrne and Kennedy She also worked last year to defeat Democrat Richard J. Daley, son of the city's late mayor and political kingpin, in the race for county prosecutor, but Daley won big, and is now frequently mentioned as a potential challenger for the mayor's job.

Recently, Byrne has been bitterly criticized for hiring an official city "etiquette adviser" at $35,000 a year But the politicians say her success with the snow may offset such problems.

"It's the first big storm since the '79 mess, and everybody's obviously making the comparison," Alderman Oberman said.