I don't have a horse, and I wouldn't try it if I could, but I also tried bicyclislinging (or Vélocifrondage in french. Fun fact, there is no direct translation of slinging in french. You shot with a sling.).
Very moderate speed, AussiePouch with my favorite shoestrings folded in 2 to have a short sling, irregular rocks picked up right before the attempt. Start with loaded sling, across the handle in a small dirt road with a lot of ruts.
First shot, low powered underhand, OK. Not my best shot ever, but it went in front of me.
Readying the second shot was a lot more tricky. So much more that I almost fell over the bike
so the second stone was picked up a few second later, and slung with my feet firmly set on our planet