Glaciers may be open although do check when their lift maintenance period is. Tignes, Kaprun, Engelberg, Saas Fee, Zermatt, Obergurgl, Stubai etc but you may well find hotels and bars closed as our half term break falls later than Europeans.
Stubai or Hintertux can be excellent. The Ziller valley leading to Hintertux is also great for walking and has more to do if the afternoons are too warm too, so you can ski in the morning and do other stuff after lunch.
we are looking potentially at the first week of Nov as DD has a two week half term and if DS ends up at the same school we thought we could try a week of glacier ski-ing.
I think I would go hotel as a treat - usually cheapie self caterers to cut costs at half term/Easter - but also as hotel might provide more facilities for the afternoons - presumably you can only ski mornings?
Have had a brief Google at Tignes (as easiest to get to by train) but would love a recommendation if anyone has done this?