Exercises to do with my barrel horse...?

So glad you asked!! The best thing to keep a barrel horse fresh is cross-training. Once the horse knows the pattern, it is not necessary to drill him on it daily, in fact, the only time you would want to run him hard is at a competition. The more 'other stuff' you can do to keep him fit and interested, the better. I suggest lots & lots of trail riding, perhaps find another discipline that you both like and branch out to include other types of competition so that the horse does not ociate competition with running barrels every time. I've found that cow work is a good thing to consider here, like team penning and sorting. Another good way endeavor is nuisance training, this is really effective at getting a horse more broke and versatile. I hope this helps you and your horse!