Idea for handling moving stealthily on a horse:
Make horse move at half speed.
On a successful Ride check DC 5, the horse makes a Hide check for the movement. If the Ride check is unsuccessful, anyone within sight range will notice the clumsy horse and rider.
Since most horses have poor Hide checks, they can only move stealthily from a distance.
You can use Handle Animal to teach a horse a trick called "hide." This trick will allow the handler to apply his Hide check result to the horse if it is higher than the horse's result.
You can also use Handle Animal to teach a horse a trick called "quiet." This trick will allow the handler to apply his Move Silently check result to the horse if it is higher than the horse's result.
The Handle Animal DC to get an animal to perform the "hide" and "quiet" tricks is 10. This must still be followed by a successful Ride check DC 5 if the handler is astride the horse.
Edit: Without these tricks, a rider cannot use his own Hide and Move Silently checks while on horseback because he is not the one moving.