My issue with riding - and especially running, god forbid - a horse in a halter is that yes, you can do it, and yes, it's freeing (I totally agree, I do it all the time on my mare) but it doesn't give you the same finesse and communication a bit would. My mare has a special bit that's only for gaming. It's a jr. cowhorse like the OP's, but a different mouthpiece. It gives her a little "lift" in her shoulder and she works good in it. She knows when she's wearing it that it's "Go time". Then she has a seperate bit for reining, cow work, etc. She knows the difference.
I don't think riding in a halter is bad, like I said I do it a lot, but you can't show in one and I like having something to help my horse's faults in the absolutely lightest way possible. It's a mental cue to her as well.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.