I think it is better to be inside. If he is worked, supplemented and then put inside in the warm his body will use the nutrients/supplementation as they were intended. If he is kept outside there will be a certain amount of shivering (temperature dependent). Thus there will be a certain amount of energies dedicated to keeping warm instead of recharging.
The dog will still be able to rest in that environment if there is a set to routine. If he comes out of the box, goes straight to his dump place, dumps and then gets put back up he can rest sufficiently in between. If his rest days are long walks where he is pulling to several different spots to try to dump/empty then that may interfere with rest. Either situation can work and both have worked for others. If you are locked in to your situation ( city/urban/country/farm) then the idea is to find what works for you and your dog. I would say make the routine that fits and stick to it. EWO