Horses are not motorcycles.
If your protagonist’s interactions with his/her gallant steed could equally well (with a change of costume) be interactions with his/her Harley-Davidson, then you have a problem.
If you don’t feel comfortable writing the horse stuff, but are dealing with a fictional milieu where horsepower is what you’ve got, then either do the research (as I’ve said here before, horse people are, taken as a group, glad to be helpful in this regard) or keep your characters indoors and on foot as much as possible.
While you’re at it, take a moment to consider whether or not the horses-as-motorcycles issue might be symptomatic of a larger problem with your story. Pre-industrial societies are different from modern ones, even if they’re entirely imaginary, and it takes doing the research (again) to get them right.