Possibly Leysin "nearish" Geneva. 1) you can get there by public transport straight out of Geneva airport (train, then funicular from Aigle) it is a couple of hours and quite a nice trip, you could probably drive it in an hour or so 2) There is a proper ski school for very young skiers opposite the leisure centre, I think they take them from 3, mine were 4, so it might be that, check. The leisure centre is a bit soul-less, but it is warm, has an eating place etc. 3) there is a great tobogganing park nearby, with dumbed down runs for the under 5s, adults love it too 4) Leysin itself is normally pretty snow sure and offers skiing for the adults attending, look, it isn't Val D'Isere, but it sort of "does the job" if you just want to do some skiing 5) we used to stay at Central hotel, it has a warm swimming pool (all on one height, so no baby pool) "multiple connecting rooms" for families, and can be B&B and evening meal, we found the food to be quite good, raclette etc. the experience is quite busy, lots of families (very few brits), but if you have young children, it can be reasonably helpful. You can also get apartments there (sep building over the way) which were a bit soul-less and basic, but to be fair, were very cheap with a double bedroom and a small room for four (and weirdly a sauna), but you still got the pool and the facilities. Main moan is you have to walk down to the ski area down a road with no pavement (ten minutes but can be tense with 4 under 12 year olds as was my case) there are ski bus etc. but was not that straightforward. The nursery slopes with a couple of button lifts used to be free and up a road just behind the hotel, but I am going back 12 years or so now a) bet the are not now free, and b) they were only any good for those that could walk up and just about ski on them (so those that can use a button lift, my youngest could manage this but only once they had been to the young skiers ski school) and even then, patchily. Swiss prices, although there is a Lidl type supermarket in the town. Ski-ing is always expensive, and hard work with young children in tow, but very much worth it to get them ski-ing in the early years, so the only worries (much) later on are about how to cope with the lift systems and the piste map. Have a great time x