I dont barrel race, but I grew up riding western. If you're converting your horse too go slowly. Teach him to keep carrying himself properly on that loose rein rather than just throwing it at him like some do. And remember that your position in western is a little different sometimes so don't beat yourself up for falling back on old habits
I do English riding but have done barrel racing at pony club and don't forget to school flying changes because they need to do one after the first barrel
Never work your horse to hard or it will start being naghty with it and always remember just have fun
When barrel racing always remember to pick up the horses shoulder. Just have fun with it!