That sounds like a little Qh mare at my old barn. She is a very "go-y" mare with an adult on her, but put a little kid on her, and she was walking slooooow. Sweet mare with no buck, rear or otherwise, but an adult had a fight on their hands to keep her at a walk if she was in just a halter, but the second a kid was on her she was stopping with the slightest pressure. It was pretty cool. Got to love the babysitter horses.
Did I mention that she is 26 and her favorite speed was "FASTER!!!!". Lol
Proud owner of ~Mana: 6yo Arabian gelding~Pearl 13yo Arabian~Danzer 14yo Arabian mare~ Tiny mini filly