I'd definitely go with layers, as opposed to a coat. Don't forget, he'll be sharing your body heat as well. You can get coats for you that go over the carrier as well, in which case you'd dress him like you plus an extra layer depending on his age.
I would say, on the babywearing sites I visit, they tend to recommend not to put baby in footed babygros, as they can pull up and be uncomfortable for their feet. Footless ones, or leggings, with some nice warm socks seem to be the attire of choice.