It is unusual, but hardly unprecedented, for men and women to have races pushed onto the same day at a major competition because of bad weather.
Seth Rubinroit of NBC Olympics noted Shiffrin became the youngest Olympic slalom champion in Sochi and proceeded to sweep the ensuing slalom gold medals at the World Championships.
Material from the Associated Press was used in this report.
Anderson's compatriot Hailey Langland, who fell on the first run but put in a solid second effort to finish sixth, disagreed.
Mikaela Shiffrin has been claiming world championships since she was 17 years old. "The girls on the podium showed that and that is why they are up there".
The wind gusts have been strong enough to push people around; by evening, metal detectors outside venues and all signage were laid down on the ground, to prevent them from being picked up by the gusts.
Of the 50 athletes in the field, only nine laid down a completed run, leading to concerns about the safety of the competitors.
Windy conditions at Pyeongchang have proven to be a challenge in the Winter Olympics.
A shortened women's snowboard slopestyle final went ahead on Monday in high winds, after qualifying was cancelled completely a day earlier.
She is expected to be one of the superstars of the next two weeks, considered a medal favorite in slalom and giant slalom, a strong contender in the combined and a possible entrant in the other two women's individual races, the downhill and super-G.
"We don't see great changes for tomorrow or Wednesday", men's chief race director Markus Waldner said at the Jeongseon Alpine Centre.
"We hope we can have races under decent, acceptable conditions".
The men's Super G has been switched to Friday, previously a rest day, to make room for the downhill.
Additionally, Svindal and Jansrud could join Aamodt as the only Norwegian alpine skiers with multiple Olympic gold medals.
The Alpine skiing at the 1998 Games in Nagano was heavily disrupted by heavy snow and rain and the men's downhill was rescheduled three times. The event was also postponed on Sunday because of conditions.
Mark Adams, a spokesman for the International Olympic Committee, said organizers were not concerned about the schedule.