Skiing at Easter with young children and a baby - where to go?

[Gem13]

DS (4) is desperate to see snow, DH is desperate to go skiing, DD (2) wants to be with her brother, and I want to be mildly amused with non-skiing entertainment with a (will-be) 4 month old baby.

DH and DS were going to go at half term but now DD wants to go too so it's going to be an en-famille activity at Easter - February will be too early post baby.

Has anyone done something similar with a baby in tow? DS could go into ski school, DD is probably too little (she will be 3 but is not the most sporty child) but could spend the morning with me and then we could all go and play in the snow, build snowmen, go sledging in the afternoon, etc.

Any suggestions?

Go somewhere high (1500-2000m at base) to be sure of getting any snow worth visiting , preferably with a glacier. However the altitude may well not be best suited for a small baby. We went to Saas Fee (1800m) in Switzerland first time when dd was around 18 months and ds almost 5 at half term. The ski school there takes them 3 hours morning session from 5 and a shorter afternoon session for aged 4 and 5's. Even then snow in the village and on nursery slopes isn't guaranteed.

The higher the better - last year Courcheval 1800 closed down in the 3rd week in March (or maybe year before), due to lack of snow.
I went to Chamonix on the 20th of March this year and snow was patchy at the bottom of runs.

Somewhere like Tignes perhaps? Then you have the glacier if you need it.