where to go for 4 nights?

What about Cervinia, lots of cruising and very good snow with more to come this week. You would have to fly to Turin and the transfer will be a bit of a pain http://www.exnetsystems.co.uk/climbing/Travel01.htm unless you book a private transfer. There are some photos from last week here: http://www.jacomet.ch/themen/skilift/album/displayimage.php?album=265&pos=53

If your committed to Geneva, Saas Fee would also fit the bill, you can get discounted rail and lift tickets via SBB Snow'n'Rail http://railaway.sbb.ch/english/snow-n-rail/ I don't think accommodation will be a problem as due to the exchange rates there aren't as many people about this season http://www.saas-fee.ch/en/reservations.cfm