Winter clothing should not be too tight or heavy. Especially for newborns, clothes that do up down the front are better than things that are pulled over the head, and can be just as snug. (Not only can it be uncomfortable for the baby to have clothes pulled over the head, they are likely to need changing so often that you need to be able to undress them quickly). You can get one-piece fleeces or other all in one winter suits which are great for taking the baby out, but still go on and off easily. Little jumpers and coats are fine too, as long as they're easy to change.
You will also need some soft hats - wool is usually best - to keep him or her warm both indoors and out, with one that covers the ears for going out (or an all in one with a hood). And of course, lots of socks and bootees.
You can see some examlples here.