While I don't know the exact criteria used to determine order (most likely random or weighted based on previous performances), this seems an ideal place to use a market-oriented mechanism! Let each skier bid on her preferred position in the order, using time handicaps. A skier who doesn't think position matters can just bid 0 across the board, while a skier who prefers to go first may bid a few tenths or hundredths of a second in each of the earliest positions. (I'm implicitly assuming a sealed-bid one round auction, but there are other models as well.)
If the assignment used a variation on the Vickrey-Clarke-Groves auction, few skiers (if any) would actually pay their full bids; only highly-contested slots would result in handicaps being applied.