You should definitely bring your ski gear.
Glacier 3000 is real close to Montreux, its one hour on the train and then you just crash at Chalet Budokan (www.demonium-mc.com).
The park is usually very good.
I would do Zermatt instead of Chamonix. They are very similar but Zermatt is more impressive in my opinion and is open for skiing!!! So you can combine the sightseeing with some quality skiing. Or you can do both, but I can assure you that seeing the town of Zermatt and the Matterhorn is one of the most amazing experiences. And then when you go up you see the glaciers of the Monte Rosa (the biggest mountain mass in the Alps). Its incredible.
Montreux is pretty sick too. Lake Geneva is an awesome place.