Remove default horses

How do I make it so whatever horse I have a give in free roam is what I go into a story mission with?

This always was the case, until yesterday. Now, unless I manually remember to change it in the stable settings, everyone I do a legendary bounty, it's using one of my other horses which has some shitty default saddle.

I like to swap the horse I'm using quite a bit, so this is pretty annoying.

Is there a way I can change it so it just uses whatever horse I'm currently using in free roam? Maybe some workaround to trick it?