Can I buy a horse for my follower?

Current mods that can allow you to buy or acquire horses for your followers to use:

Original / Legendary Edition (PC)

Mounted Followers

...this mod once installed lets your follower have and ride a horse that will spawn near your last ridden horse. It works with stolen horses, quest horses, but of course works best with stabled horses.

Note:
1 - I suggest you to never mount the follower horse, it may result in the follower mounting yours and after you dismount you'd have to catch your horse that tries to go back to stables.
2 - You can fast travel but note that your follower may not be teleporting with you if you were mounted, IT IS NOT AN ISSUE tho your companion will come back after a while (specially if you transition to doors etc)
3 - Once their AI kicks in followers are rather slow (they walk) to catch their horse ( just go.. they will catch up ).
4 - The AI will not enter combat unless you dismount and so the normal behavior starts. 5 - If your follower is very close to you and you dismount, they may not dismount at first... but once you start moving they will.
6 - Follower horses are not owned by the player so they will show with Red name.. this is totally normal! they are not supposed to be mounted by you!
7 - If for some reason follower horses aren't showing up, mount up on your horse and then dismount.. in few seconds follower horses should show up.

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Horses For Followers

Horses for Followers will make new horses available to buy at all the main stables Better Follower Improvements will enable your companion to ride them and follow you. To make followers mount their steeds, all you need to do is mount your own and they will follow suit. When combat ensues, they will dismount and engage in combat as normal. The horses are set to avoid combat if possible, unlike the vanilla player's horse. Now that you have two horses to pay for, you will appreciate their increased survivability.

The horses will be owned by the current Follower Faction or Player Faction, which means that even if you change followers, there is no need to buy a new horse for each one.

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Horse Branding

Mark any horse or mount for followers to ride, mark them for yourself so they are not stolen, stop them from going away when you dismount and similar expanded control..

Horse Branding has been tested with TCG Extended Version and TCG + Multifollowers combo. Meaning if you want to ride around with a dozen followers use the said mod combo!!

With the Horse Branding mod, you can make your follower ride non-horse mounts (like Mammoths and Wolfs) with this mod: Like a Boss.

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Special Edition (PC)

Convenient Horses

Convenient Horses for Skyrim Special Edition is... aiming to overhaul the horse system in Skyrim. Unlike its predecessor, it has been built from the ground up to radically change the way you interact with and use horses...

Features

• Mounted harvesting of ingredients.
• Mounted interaction with people and corpses.
• Mounted combat horse charge.
• Horse stabling, naming and quick swapping.
• Horse encumbrance system and mobile storage. Horse dialogue interaction and fast dismount.
• Horse follow and combat behavior customization.
• Horse whistle and calling.
• Horse attribute training. Horse equipment crafting and discovery. Followers’ horses and mounted combat.

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Immersive Horses

Immersive Horses is a lightweight overhaul for the horses in Skyrim built on SKSE64 and SkyUI SE. The goal of Immersive Horses is to improve on nearly every aspect of Skyrim's horses while remaining as true as possible to the original game. Immersive Horses adds a range of new commands and related options for horses as well as an integrated ownership and follower system designed specifically for horses.