Chunks don't load while riding a horse, unless they are started loading while not riding.

Example: your horse is in an unloaded chunk. Run as fast as you can (or teleport) to your horse, and sit on it. All the chunks around you will load, because they started to load when you didn't ride the horse. But if you ride to the edge of the loaded chunks, the unloaded chunks will not load.

(ps: sorry for my bad english)