Originally Posted by Cygnus Q'ol
It's OK. I actually like being on foot better anyway. I can negotiate hills and rocky areas better without him and I love swimming.
I would imagine ahletics don't increase while riding either.
There are no skills governing or being affected by riding, for some weird reason. Athletics do only increase if you run around on foot, and acrobatics increase if you jump (or do evasive rolls I think).
I prefer moving around on foot as well, not just because it helps you increase two skills, but because you have better control of where you're going and can respond more quickly to hostiles showing up. It's also easier to sneak up on bad guys if you don't have a huge animal in tow.
At 100 Speed and 100 Athletics you run significantly faster on foot than most horses anyway. (And you can bump those stats above 100 with potions and enchanted gear as well as some quest rewards.) My character can run past those Black Horse Courier riders you can encounter on the roads on Anvil and Leyawiin.
Having a high Acrobatics skill is very handy for getting around, taking shortcuts in towns and climbing up steep mountain sides or generally getting up somewhere where melee enemies can't reach or follow you. I love those evasion rolls it enables you to do as well.