I would think it kinda depends on how heated the current barn is. Around here most heated barns are just warm enough to keep pipes and water buckets from freezing but are still pretty darn chilly inside. If your horse is blanketed now in the heated barn maybe switch to a lighter weight blanket for a few weeks to harden him up a bit. Also, give him plenty of turnout time in an appropriate blanket before the switch to get him acclimated to the real world temps.
These are just hunches because I've never had a horse in a heated barn.