Should i clip my horse and/or how?

I have had my horse for almost half a year now and I am just recently now starting him through training. He rides in an indoor arena and is kept stalled daily. The trainer works him pretty hard for an hour or two about 4-5 days a week. I personally ride him or lunge him for an hour or so the days the trainer does not work him. He takes about 30 minutes to cool off using a cooler after workouts and he is blanketed the rest of the time. I have left his coat alone so far but with his workouts becoming harder and longer I am debating whether to clip him or not. He does get fairly sweaty and since there is no cover on his winter blankets, his neck is furrier and does get more sweaty. His muzzle and his bridle path have been left unclipped. He just got shoes so he does not go outside anymore with the other horses. I will be starting him in shows within a month or two. Should I clip him or not and/or how should I clip him? If not, how should I help make sure he is warm and comfortable and also cool after his workouts?