I think you understand it right "luffy". Two meanings can be obtained from the sentence. It can mean that we get on horses and ride to a location. It can mean that we go to a location and get on horses there. Let's consider the prepositions, TO and AT. Usually, Native Speakers would never use either preposition in the sentence, because it would not demonstrate proper grammar.

Yes, I agree with Ben that ' Can we ride horses there?' only really has one meaning. You're talking about a particular location, perhaps a tourist resort, and you want to know what you can do there. You're keen on horse-riding, so you ask this question. 'Ride horses' is an activity, not a means of transport. If you want to know if this location is accessible on horseback - for example if there are suitable tracks leading there - then you would say something like 'Can you get there on horseback?'. This is a different focus. Neither of your alternative sentences (at there/to there) sound natural at all. A native speaker would be unlikely to say either of those.

Where I come from, that sentence has only one meaning: At that location, can we ride on horseback? If we wish to ask, "Can we go there on horseback?" we can alternatively say, "Can we ride there on horseback?"

It's not correct to include a preposition before 'there'; but otherwise your understanding's correct. The sentence could mean two things.