Yes, you can. I can not say if permanently or not, though. My best guess is no.
I've just recently lost Lydia (her bed in my house is still "owned" though, maybe I should go look for her.. maybe she needs my help!), one of your first companions. When riding, she frequently started attacking random crabs and thus falling too far behind or her pathing was just so bad that it took her forever to find to me.
If you are really attached to your follower, you should play it out and wait for them. You can also tell them to wait for you somewhere, ride to your destination, then use fast travel to get them.
Lydia simply despawned for me several times when I rode away from her and upon changing the zone she re-appeared every time. But then just recently, she was gone entirely and I can not figure out where she is or if she's even still alive. But that's really my fault I guess.
Any follower that is skilled at light armor and sneak (and optionally, archery too) should be fine. Followers should preferably be non-mage, as casting spells will attract enemies and blow your cover. Complete list of followers and their descriptions here: http://uesp.net/wiki/Skyrim:Followers
Followers that are good at sneak, light armor and archery are: Aela the Huntress, Cicero and Dark Brotherhood Initiate.
Tips to make followers extra-sneaky:
- Have them wear light armor only, as heavy armor is noisier and makes them more likely to be detected.
- Give him/her an item that has the Muffle (wearer is muffled and moves silently) effect (usually a boot or a
shoe; and usually light armor too).
- Have you follower wear apparel that increases sneak skill (Fortify Sneak).
Also, note that (from the UESP wiki's "Skyim Followers - Follower Stats" article):
A follower levels up according to the PC's level up to the follower's maximum level (which varies for each). With few exceptions, each follower has a maximum level, and a specific set of primary skills, which are dictated by their class.
Prior to patch 1.6, a follower's skills, health, and other stats were set when they were first spawned (which is typically when you enter their starting cell, become a Thane, and so on) and would not increase as their level increased. Prior to the fixing of this failure of stats to update with patch 1.6, players could update a non-essential follower's stats so they would increase based on their current level by using the Wabbajack to polymorph them into another creature, after which their stats would update upon recovering their original form. Players of the PC version could also use certain console commands to fix any follower's inability to update their stats with each level.
So in most cases, leveling up the player character will also make your follower level up, increasing the follower's sneak skill (the maximum and by how much, will depend on the specific follower and their NPC class).
Best Answer
Current mods that can allow you to buy or acquire horses for your followers to use:
Original / Legendary Edition (PC)
Mounted Followers
Horses For Followers
Horse Branding
With the Horse Branding mod, you can make your follower ride non-horse mounts (like Mammoths and Wolfs) with this mod: Like a Boss.
Special Edition (PC)
Convenient Horses
Immersive Horses