We've been playing in the cold and snow of western NY for 5 years now. Sometimes with wind chills well below 0. We have different levels of polypro undergarments including socks. A neck gaiter vs. a scarf is priceless. Polar fleece or something similar is indispensable as outer wear. And some sort of muffler for the hands like football players or hunters use is a must. Except in the most bitter cold and even then rarely do I wear a glove on the throwing hand, so between shots a couple handwarmers inside that muffler and I'm good to go. Insulated waterproof boots are a must.
This year I'm considering gaiters for the deep snow and muck of late winter early spring.
We have all the necessary gear already except a new box of handwarmers.
Oh and laslty and perhaps most importantly, now is the time to start concentrating on following every shot, yours and everyone elses, to the ground. Nothing is more important than a keen set of eyes in the snow.