I don't know which horse you are using, but the ones I have are from the Horse and Tack pack.
If I load the horse and then right-click, I see an option Operate with three choices: Saddle-Mount, Saddle-Dismount, and Saddle-Ride.

If you have a character loaded and select Saddle-Mount, the character will mount the horse.
You may have to make some adjustments, but the basic animation is there.
NOTE: You have to make sure that the character is facing the side of the horse, otherwise he/she will be walking in circles.
In case you don't have a horse with these options and you don't want to buy the whole pack, you can get a single horse from the Reallusion Market Place. For example this white one. With one horse you can make different kinds by changing the textures.