Yes, Clydesdales are riding horses along with work horses. They can be used for virtually everything except racing. They don't make the best jumpers either.
Both are great horses to ride. The wild mustang program offers Mustangs for very little money. They have a few regulations you must follow to get one of these horses, but they are available and offer...
It all depends on the stable. If you could specify the stable I could tell you. Often you can request horses, and at some stables you ride the same horse for every lesson. But if your riding that...