Hey OP, I live in Geneva and have explored some of the local resorts. I love Combloux (next to Megeve) - it's stunning, the most beautiful charming resort. Lots of green, blue runs, wide easy slopes, beautiful chalet restaurants on the mountain, my favourite resort ever!. I skied there 2 weeks ago and it hadn't snowed for 2 weeks before that, it was hard packed snow, icy, I saw people being helicoptered off the mountain after stacking it on blue runs. But I felt safe on the blues because they're quite flat. I do think at Christmas time you have a pretty good chance of snow. I was in Morzine at Christmas, we had snow. If you were going in February I'd say go somewhere snow sure. I went to Morzine at Feb half term this year and it was absolutely terrible. Warm, raining, no snow, packed.
I'd really think about what you're looking for. I personally don't like big, heaving, ugly resorts like Morzine, Avoriaz, Flaine or Chamonix, i dont want folie douce, big queues for the lift or people bombing it down the slopes pissed. I prefer something charming, more French, beautiful views, not crowded, easy to get round. Love Combloux. La Clusaz is very beautiful and charming. Gondola lift from centre of town takes you up to the beginners area and a beautiful view, accessible for pedestrians, restaurant with amazing view. And then in the village centre they have daily entertainment over Christmas, shows, music. Les Gets feels very English, and a bit more upmarket than Morzine, it's more compact too, I like it. But again it's not high up.
If you can go anywhere maybe look at Val Thorens, Val D'isere, Verbier for higher resorts if you want to be snowsure. I personally think at Christmas time you'd be alright.
Saint Gervais and Les contamines are next to each other and worth a look. Les Contamines I love for skiing but no idea what the village is like. It has a great set up for beginners though, and stunning views. Big playground on the mountain in the snow for the kids. Snack bars on the slopes as well as restaurants.
Les Carroz is meant to be lovely but I've not been there yet.