Not really, a lot of the encounters are underground or in buildings, or otherwise situated where being mounted won't give you any advantage.
From my experience we spent a lot of time going into caves, old buildings, and other places where a large mount isn't going to work. Now you do want a mount to travel on, because you are exploring a lot territory.
From my experience, note that I'm only level 3 almost level 4, we've been outside for about 75% of the time. There are indeed some caves, underground places and buildings that you will more than likely need to go into (important missions and whatnot).
Note however, that when you get further into the books and further in level, there is more chance you'll be in cities, buildings and again possibly underground.
Besides obviously having something to do with mounts, I'm not all that sure what the horse lord is actually capable of. In either case, try to have a well rounded party if at all possible. (Not saying to give up what you want to play as that comes first, but a well rounded team can definitely help.)
There is a lot of exploring outside early on in the adventure path. However, there is still a lot of dungeon diving as was mentioned.
I would say that if I were going to have a mounted character, then I would like Kingmaker or Jade Regent (especially the third adventure if the mount can survive the cold). This is oppsed to Skull and Shackles were I would not suggest a mount unless you can get a Roc or an aquatic beast of some sort.
Rangers would work well in Kingmaker as you have to search hexes and such to clear out the land and eventually claim the land. All our characters were mounted for at least half the adventure, just maybe not inside where the action was happening. There is also some warfare rules that would be fun to have a mounted character involved with in my opinion.
In my (still limited) experience with Kingmaker, being mounted doesn't help you all that much in exploring either, as much of the terrain is dense forest where you apparently can't travel by horse.
It is mixed, so don't sink all of your resources into it.