Do I need a bigger size pouch to use in the winter?

For winter use, most people wear the sling and the baby under the coat.    You could get a larger sling size to wear over your and the baby’s coat, but how much bigger would be hard for me to determine, since I don’t know how big and bulky your coats are.   I personally find it uncomfortable to wear a sling that is too big, and I find it restrictive to wear a sling over a coat.  Babies are generally more content when worn next to the mother’s body, and the mother’s body heat keeps the baby warm, which eliminates the need for a very heavy coat for the baby.  Here are a couple of pics with my daughter, she was about 10 months old:

She has a hooded poncho on, and my coat is zipped around us.

She has the same hooded poncho on, and I have a wrap like winter coat over both of us.

There are coats and vests specifically made for babywearing, that have a head hole for the baby, or zip out panels to make room for the baby.   Any oversized coat will work though.