Does Shadowmere and Frost behave like vanilla player horses when you ride a different horse?

The main player horses have a condition to check if it is the last ridden horse. If not, off it trots back to the stables. Does Shadowmere and Frost have the same kind of behaviour? I looked on the Alias and base shadowmere horse, but found no AI with the GetPlayersLastRiddenHorse condition. Although it could be in a script I have not seen yet.

I lost shadowmere and he just stayed where I lost him, if that helps you

Thanks. Hope you got him back

I did, but i had to cheat and use the MoveTo console command to move me to him haha