In reply to Jim Houghton:
Going over 4000m at that time of year is a serious undertaking. It's certainly possible but not to be underestimated. The days are short and it is bitterly cold, and storms are fairly regular. Seriously think about frostbite, and the consequences if you get caught out in bad weather. Avalanche conditions are less predictable that early in the season and snow bridges on crevasses could also still be weak.
If you're set on summits on skis I would personally be thinking more about the 2000-3000m range.