In winter, thankfully, this isn't a problem. I prefer a stocking-type cap with ear flaps for very cold weather. On more balmy days, I'll often use only a fleece headband to cover my ears. Remember, if your head is warm, you'll hold the heat in your body better. Getting around through deep snow can be challenging, even if you are in great boots.
Snowshoes offer a great solution to the sinking-in problem.
Although they take some getting used to, in relatively little time you can get around on them with ease and get where you want to go for your photograph. Cross-country skis are another solution, although they take longer to master than snowshoes. The choice depends on your photographic goals for that day. In either case, be sure you carry emergency survival supplies with you if you're venturing into the landscape alone. If you follow the above suggestions, you can have a wonderful time outside photographing the magic of winter, and come home with terrific frozen images of your own.