A lot of people in Geneva head to the French Alps instead of the Swiss Alps because they are closer to them. The larger resort towns would be Morzine and Chamonix, but there are lots of nicer, smaller, places scattered all over. Unfortunately, there's not much snow right now unless you get pretty high up.

The closest hot baths to you that I know of are in Yverdon-les-Bains, but they are not surrounded by mountains, which is often part of the charm of these places. A lot of people in Lausanne instead head to Lavey-les-Bains.

Your 4 year old should love some of the Escalade events. I'm not aware of everything that goes on during the weekend, but you should take him out to watch the short, costumed, running "race" on the Saturday evening / late afternoon, which is called "La Marmite" I believe. Lots of families take part with very elaborate costumes. Maybe you can starting making plans for what you'll make to wear next year.