I just bought a pretty nice horse and I wanna keep it as long as possible. If I fast travel to an inn and sleep and save will it be outside waiting for me?

Yes!

yea, whenever you fast travel the horse goes with you. if you fast travel into a city, the horse will wait in the city's stable

My character has had her horse well over 500 hours and has learned some good tips. Here are a few vanilla ones:

Something that can be helpful to keep your horse alive while traveling is to ride with lots of detect life range. That allows you to avoid surprises so you can ride around trouble, dismount and take care of it on your terms or simply get a head start in outrunning trouble.

A walk on water spell can help your horse cross water very effectively.

A command creature spell can recall your horse to you from within sight.

A weak but long lasting fortify speed spell on your horse can have a pretty dramtic effect.

:foodndrink: