Eurosport is the way forward, it seems the only channel with every winter sport on the planet - from skiing to bobsleigh. I am glued to it all winter, but it is the only one that I know on the sky / Euro satelite networks that shows all the skiing from now till the end of the season.
According to the ski schedules there is nothing this weekend, Eurosport UK - in the winter sports section - have a list of the FIS Ski dates under “calendar” - http://uk.yahoo.eurosport.com/alpineskiing/world-cup-1/calendar_sea83.shtml - if the races aren’t cancelled they will be on - usually live - mostly at the weekends obviously hope that helps!
eg: - check the schedule for next weekend and the skiing is on “live” at various times and it also tells you the event showing from Levi