I have a horse. Lydia does not have a horse, and is therefore painfully slow - Is it possible to get one for her or the other followers? If not I will be somewhat annoyed.

No, because they don't have the option to mount the horse... instead the option when you tell them to interact with it is "attack." Horses are so much trouble right now that I'd rather just have the followers able to teleport to you if they fall behind.

I think what would be a good idea with followers would be that they walk exactly where you walk and at the same speed. Yes, it may look a little weird sometimes, but it will remove all the stupid glitches where the followers get stuck on rocks etc.

Big thing that I've seen about followers being slow is that they don't want to try to jump over or jump off stuff, they just run around.

Hmm, I find my horse to be much less irritating than the ones in Oblivion - I lost count of how many times it ran off after a fleeing wolf or something while I couldn't keep up. Then got munched by a troll. Bethesda can't possibly think a system whereby your follower has to slog it on foot behind you and your horse is a good one, surely?

This is very fun if they pull a lot of enemies towards you.