I'd say running in the cold weather would be better for conditioning. You're forced to push harder in those harsher conditions. I believe it's because things contract in cold, in this case your lungs, so you don't get as much oxygen.
I'd say the fresh air from outside would be better anyway, and it's nicer to get various scenery rather than being exposed to the same shit over and over on a treadmill.
Just saying the things I feel would be pluses. Ask your coach why he thinks running on the road would be more beneficial, maybe there's other reasoning.