If you're going to learn mounted games, then the only way you can really mount during them in swinging up from the ground. This is a lot easier on smaller ponies, which is one of the reasons why they tend to get used more than horses. It is possible to learn to jump onto horses from the ground though. Jockeys do it all the time. It just takes time and patience. If you have access to a smaller (quiet) pony, it might be worth first learning on it.