Made from 2-3 leather straps and a couple of nuggets, reins would become a semi-permanent part of the horse, like saddlebags. When you dismount a horse with reins they are automatically tethered to you (so no more wasting two inventory slots to carry a rope), a hitching post would work normally. If the scripting isn't too complicated you could even tether a horse to a tree or shrub. And since the player can hearth and their boat can "dock" to home, perhaps a horse with reins could have a home hitching post to which they could return if separated from their owner, either on command (hearth magic option), automatically if player hearths, or after a certain time or distance. When right clicking a hitching post you would get options to "tether" or "assign", the latter would make this the "home post" for that horse, if you own that post.
Another possibility, the q of reins could have a small buff on the speed and/or stamina of the horse.