As rain drenched the drought-stricken Bay Area on Monday, skiers and snowboarders also had reason to rejoice: The early snowstorm in the Sierra — and the cold nights — have hopes soaring for an infinitely better ski season, a relief after years of bitter disappointment.

“Exuberance would be far short of what people are feeling in this industry,” said Bob Spees, general manager of the Lake Tahoe-area outfitter Powder House who said last winter was the worst skiing he had seen in four decades.

By the time the storm passes Tuesday, it is expected to bring up to 8 inches of snow around the lake and more than a foot at some high-elevation peaks — not a major snowfall but enough for Heavenly and Northstar ski resorts to announce they would open Saturday, six days early, and to post celebratory photos of snowcat vehicles taming piles of snow.

“The cats have been uncaged!” Northstar tweeted in anticipation of the storm.

Excitement over the snowfall comes amid years of drought and warm winters that have decimated the Sierra snowpack. In normal years, California counts on the snowpack for 30 percent of its water supply — and Tahoe counts on it for tourism. The number of winter visitors to 25 ski resorts in California and Nevada plunged from 8 million in the 2010-11 season to 5.2 million last season, according to the California Ski Industry Association.

The National Weather Service’s Reno station issued a winter-weather advisory through Tuesday morning. The storm system that moved south from the Gulf of Alaska brought cooler air and heavy rain to the Bay Area on Monday. It also lit up the skies with a rare thunder-and-lightning show, including a dramatic strike right by the Golden Gate Bridge. The bridge itself was not hit, according to the transportation district.

The rain fell with intensity, but it also passed through quickly, leaving a half-inch or less in much of the Bay Area.

Parts of Gilroy and Morgan Hill got soaked, with more than an inch of rain, the highest total in Santa Clara, Contra Costa, Alameda and San Mateo counties. In the East Bay, Lafayette recorded 0.78 inches of rain and Livermore 0.62 inches in the same 24-hour period.

Residents should expect dry, unseasonably chilly weather in the next few days, said National Weather Service hydrologist Mark Strudley.

The National Weather Service has not issued a frost warning for the Bay Area, said meteorologist Rick Canepa, but it is possible that the dry air and long nights will bring temperatures below freezing in some places, such as wind-protected valleys.

The cold air is also setting in across the mountains, another good sign for the slopes — and an economy that depends largely on tourism.

“Resorts are desperate to get a good foot forward this year,” said Mark McLaughlin, who has written books on Lake Tahoe, winter sports and skiing in the Sierra.

Thanksgiving weekend is typically the start of the ski season, but recent snowfall has allowed some resorts to get started early. Boreal Mountain Resort had two lifts running Monday, and the top of its runs are open, according to the resort.

Mt. Rose in Reno opened Wednesday, and like others in the industry, it hopes to capitalize on the weather pattern expected to bring more rain and snow to California this year.

“El Niño is coming. Get your season pass today!” its website announces.

While this week’s snowfall may not be massive, it should be enough to cover the rocks — setting the stage for a good year of skiing, said McLaughlin.

“Ultimately,” he said, “it’s going to be looking like winter after this storm.”

Staff writer Julia Prodis Sulek contributed to this report.