For family reasons I have an opportunity to get four days skiing
before Christmas (20-23) anywhere within easy reach by train of both a
big airport (Geneva/Zurich/Basel) AND Basel city.

Train timetables seem to suggest in order of distance Engelberg,
Wengen, Crans Montana or St Anton. Where are we most likely to have
decent snow that early and be able to find a hotel that doesn't insist
on a Christmas booking?

Or is there anywhere possible on a daily commute from Basel that will
have snow?