I don't do barrels, but I do pattern work. Yes, starting slow is good so that you aren't just running blind, but there is a point where you can't just let the horse be a mindless drone.
The veteran Games horse at festival knows the games we play as if his eyes were closed. But the second its "show time" you better have your game on or else he takes advantage. Cuts corners, gets sloppy, etc. And this was my folly in simply relying him as a mindless drone. It landed me in a face full of dirt because I was expecting him to be reliable and simply "do his thing." Nope. He cut the corner suddenly and I wasn't expecting it and down I went. In front of an audience.
None the less, we walk trot and canter a few times to get the pattern down so they have an idea of what is expected. From there, we up the ante and go for it like we would for real.
Edit: And mind you, Shooter is a 20 year old bomb proof gelding who we consider our babysitter.
^^^THAT is what you DO NOT want to do when training a horse.......no matter how old the horse is. It takes roughly 2 years before a horse is ready for speed. It isn't all about speed and how fast you can go. You need to properly teach the horse HOW to do it CORRECTLY and that takes time.