There are two Christmas markets in Montreux - a very large one along the lake with over 150 stands, restaurants, etc, and a medieval one at the Château de Chillon on the weekends.
In addition, there is a "Father Christmas village" at Caux and "jolly old Santa" himself is up at the Rochers de Naye.
Here is a link to complete information about all these events:
I go to the Christmas market at Montreux each year. And each year it is bigger and better. From a smallish market strung out along the route cantonale it now occupies most of the lakefront promenade in the town. Last year I took my grandchildren to Caux to the Santa Claus village. They (2 and 4 at the time) loved it. There were elves, reindeer (live ones!) games etc. It was great fun. This year we plan to go all the way to the top at the Rochers de Naye and visit Santa himself.
The site suggests that seats be reserved in advance. We did not do this last year and had no problem getting on the trains we wanted. And I actually saw no sign of seats being reserved... I would suggest that if you are interested you just go! There is an hour beween arrival of one train and departure of another at the top and that will be plenty to meet Santa, see everything, have a hot chocolate etc.
Trains to Caux and the Rochers de Naye leave from the Montreux station. For times etc see www.mob.ch