I think the answer to that question depends on how far along the horse is in training and what stage of competition you're in. If your horse is finished and you don't have a big event coming up, then I'd go with most of the suggestions you've already heard. Keep him light and relaxed. Lots of long trotting to keep in shape. Hill work is great if you have access to hills with good footing and no holes.
If your horse is green, or you have a big show/rodeo/futurity or whatever coming up, there are a lot of exercises you can do. Straight barrels are great, especially for finishing turns. Slow work, stopping where you want a rate and exaggerating pockets can be helpful. Sometimes I trot or lope big circles around a barrel until the circle is round and relaxed, then turn the barrel. I usually stop a stride or two from the barrel before I ask him to move off again.
The key for me is to keep everything relaxed and not over do it, no matter their level of training. DON"T take him through the pattern every day. A barrel horse will always be a horse first. I like to do lots of trail riding. Moving cattle is an excellent thing to do, too, if you know anyone who needs that kind of help. Don't make the horse get bored or sour on barrels (or poles or whatever else you might be doing).
Learning never stops