Thanks for your replies! Getting it off was less of an adventure than putting it on, for me. I removed the sleeves from my arms, then untied the mei tei and then removed the coat from baby's head.
Getting it on? The only way that I have been successful so far is from the top upwards... I kind of bring the back of the coat up from my legs towards my back, until it reached the part where baby's head goes through, and then put the sleeves on. It takes a long time

. Trying to put the coat on a more "normal" way, DS simply prevents the coat from coming anywhere near him.
Another concern - once it's on, he likes to put his arms through the hole as well. The whole point of the coat was one coat keeping the both of us warm, because the baby coat in the mei tai feels, well, uncomfortable and really bulky. But if he keeps putting his arms out, he'll be cold.
Any other suggestions? How do you make babywearing work in the winter? For front carries, I just wear a coat a couple sizes too big and we have no problems at all. But my back wants a break from the front carry at times

.