Austria's Marlies Schild held a narrow lead in the delayed women's combined after two slalom sessions with the downhill still to come in San Sicario.
Schild holds a narrow lead over favourite Kostelic
Schild clocked one minute 21.22 seconds to edge Croatian defending champion Janica Kostelic by just 0.46.
Austria's Kathrin Zettel lay in third with title contender Swede Anja Paerson fourth and 0.84 off the lead.
Briton Chemmy Alcott was disqualified after a solid first slalom run because her skis were deemed too narrow.
High winds forced organisers to call off Friday's downhill for safety reasons after Nika Fleiss, the first skier down the course, was blown over by the wind.
The start of the race had already been moved to the super-G line, 500m lower, and delayed by an hour because of swirling snow.
Kostelic delivered two efficient but cautious runs, just days after suffering from a higher than usual pulse rate which caused her to miss Wednesday's downhill final.
The Croatian had a thyroid operation two years ago, and her health has been fragile ever since.