Question - are you riding in a heated indoor arena?
1. If you leave him hairy and ride him inside he's going to heat up fast and sweat more.
2. Now you have the issue of a horse who is hairy and sweaty/damp - drying him is going to be a PITA if not impossible, which opens you up for skin issues. Fungus loves damp warm sweaty hair and skin.
3. Are you going to turn your horse out into the conditions damp?
1. If you're riding inside your horse is going to be more comfortable and cool out faster and be at less risk of skin conditions.
2. You should offer his clipped areas some protection from the conditions, if you've belly clipped look for a rug with a belly flap. Be prepared to double rug.
3. He will need some more forage.
I trace clipped my Reiner (haha) last year and he did fine with extra rugs. Here he is trace clipped image.jpg