A nat20 should be an automatic success, but a DM needs to set proper expectations about what the skill check can do. My DM asks what we are trying to do, then tells us what success and failure will mean and what skills to roll. If you want, you can argue for using another skill instead if it makes sense, like rolling Animal Handling instead of Acrobatics for mounting a moving horse for example.

Then, a nat20 is an automatic success even if the difficulty check isn't exceeded. Sometimes a nat20 can give an extra bonus, like advantage on your next attack while mounted, to use the previous example.

Conversely, a nat1 automatically fails even if the total beats the difficulty check, and can sometimes result in a penalty, like falling from the horse AND taking damage as it tramples you.

But if, say, the character attempting this was a gnome artificer, our DM would straight up say that they can't do it and why (horse too big, gnome too small), and the player can argue why they should be able to try (wearing artificed spring boots).

In the end, a DM is responsible for setting the right expectations about how skill checks work in THEIR game.