Sen. Ernest F. Hollings (D-S.C.) yesterday became the first Democratic presidential contender to announce a full-fledged committee of supporters in Virginia, a state whose Democrats have been reluctant to take sides in the 1984 contest.

At the head of Hollings' Virginia campaign committee is William B. Spong, the last Democrat to serve the state in the U.S. Senate, a figurehead for the party's moderates and now dean of the George Wythe School of Law at the College of William and Mary.

Also backing Hollings are former gubernatorial candidate William S. Battle, and Del. Mary A. Marshall of Arlington, the first Northern Virginia legislator to publicly endorse a Democrat in the 1984 presidential race.

Formation of the Hollings committee is one of the earliest signs that presidential campaigning is picking up in Virginia, although most politicians--including the ranking Democratic officeholders--are expected to remain on the sidelines through the fall, waiting out the state's legislative races.

Campaign workers for former vice president Walter Mondale, who made an appearance at a Young Democrats function in Arlington last spring, say they expect to announce a steering committee in Virginia by early October. Mondale already has the public backing of Rep. Frederick C. Boucher, a Democrat from Southwestern Virginia, and of his Washington law partner, Arlington County Board Vice Chairman John Milliken.

Sen. John Glenn (D-Ohio), viewed by many as a comfortable choice for Virginia's conservative Democrats, has been in the state three times this year. His most recent excursion was to a $1,000-a-head fund-raiser in Virginia Beach organized by Dr. Ronald Dozoretz, a wealthy Democrat who last year served as finance chairman for Lt. Gov. Richard J. Davis' unsuccessful Senate campaign. The Virginia Beach function is expected to net the Glenn campaign more than $40,000.

None of the campaign groups expects an early nod from Gov. Charles S. Robb, who this summer was reported to be privately backing Glenn in conversations with other governors at the National Governors Conference. "I can say that Robb is not committed to anybody," said Mark Emblidge, deputy Glenn campaign manager, "and we do not take it for granted that he will commit to us."

Hollings' backers are hoping his appeal as a fellow southerner with a history of backing the military and espousing the conservative fiscal policies favored by many Virginians will boost his name recognition in the state.

"I think he is the cleverest of the candidates," Marshall said. "He's by far the best on women's issues and he was gutsy enough to vote against the Reagan budget."

But like most other state legislators, Marshall said she expects to have little time before November to devote to any political activities other than her own reelection. All 140 of the General Assembly's seats and many local offices are up for election this November.