The movement and jostling of a horse interrupts your concentration for spellcasting.
The same can be said for landing shots with a bow, but with skill both should be possible. They were just lazy, is what it sounds like to me. I'm not going to complain because I'm happy they even added what we have now, so I'm thankful, but there is no excuse for not being able to use magic. At the very least, they could have just limited magic use to targetted spells, and make it so that we aren't allow to cast self-target spells. (If they find self target spells on horseback OP for whatever reason). This way we could at least deal ranged damage on horseback.