Nope. I had my daughter in early February (was supposed to be early March though) and we never had one or needed one. Just dress your baby appropriately for indoors and use a jumper and blankets when you go out for walks. Unless you are going to be spending lengthy amounts of time outdoors in very cold weather (which you probably shouldn't do in the first month anyway), a snow suit is likely going to be too warm for just going from house to car or car to shop or for brief walks around town in and out of shops. And you'd end up having to wake your baby to undress them if they're asleep because a snowsuit is too hot for indoors.
One thing we did find that was nice was a fleecy carseat cover. I have no idea where you'd buy one (my aunt and uncle in the U.S. sent it to us!), but it's basically a fleece lined cover that fits over the carseat, with an opening in the middle. It was great for going between car and house on cold, windy days as it blocked out the wind and kept warm air inside. I think you can leave them on for walks as well, but we never did. Just used blankets. Or a wrap (your body heat is much better for baby than layers of clothes).