Alrighty, to get things straight, I do most of my riding on grass. But never do I work on barrel racing stuff faster than a trot on grass. It just doesn't work if they can't dig in and actually USE themselves. To teach a horse to properly turn barrels, an arena with footing is your best choice.
My horses have all pasture sorted cattle, pasture roped, chased run-away cattle down and turned them, ect ect, but it's not a consistent every day thing like working the barrel pattern would be. The biggest stress of working barrels on grass is the repetitive stress of the same thing over and over. Going for a little rip on grass and pulling a tight circle probably isnt going to hurt anything, trust me, I grew up riding my horses on grass/stubble fields, I know what it's all about.
That's fine, it was just sounding like you where saying a horse can ONLY be riden in an arena. That's why I was tryng to clarify.
As for comparing barrels vs. c-country, they're the same but different. Depends on the course how tight turns need to be and at what speed. Is it a barrel pattern, no. But it can be just as physically taxing on the joints.
And third (why I didn't think of this earlier), I don't know anyone who actually RUNS the actual pattern at home. So in my mind, and in the circles I ran in, training on grass would be a non-issue since the pattern is never worked at more than an easy canter anyway.