There is a large area of riding stables on the east the Venoge river near Lake Geneva - just on the northern side of the lake road between Lausanne and Morges. I've cycled by many times and it looks like a pretty big place, sorry I can't give you an exact location.

I also nearly always see people riding horses in the Boit de Jorat, the large forest north of Lausanne which Chalet a Gobet is in the middle of. I don't remember noticing riding stables nearby, but I expect there must be some somewhere near there.