Not exactly the same as this. EDIT: The solution to that question involves killing the horse. Shadowmere is immortal. This is not the same question.
I have gotten far enough in the Dark Brotherhood that I have been gifted with an immortal horse. The problem is, horses in this game seem more of a burden than a help, especially since Shadowmere seems intent on reporting any crimes he sees me commit.
Can I stable him somewhere so that he doesn't follow me around every time I fast travel? Is there any way to get rid of this annoying (and creepy) horse?