Like others have indicated, this opens a whole new topic - how to travel outdoors safely in cold weather, which is probably best left to a dedicated thread on an outdoor-related forum. Here are several things I do that are specifically related to photographing in the cold.
1)While traveling (bc skiing, snowshoeing, or hiking) I am adding/removing layers as conditions dictate. If it is really cold (winter, not spring), then when I stop to photograph something, the first thing I do is remove my pack and put on a down parka and down mittens. The mittens are expensive expedition style down mittens ($!). I put a Costco handwarmer in each one and secure them to my arms so that when I remove them they hang free. I can do most things I need to do with the camera with the mittens on, but inevitably one will need to come off. Depending on the temperature and how much wind there is, they can stay off for up to a minute before I need to get my hand back in. Sometimes if it's windy then ten seconds is about all I'm willing to expose my fingers. This works well for me. It is easy to tempt frostbite when you are excited about getting a shot.
2) I leash my lens cap as well as my mittens. A simple task like removing a lens cap and putting it in a coat pocket (which needs to be unzipped then zipped back up) is far more difficult when it's cold and you have gloves on. Ever drop a lens cap in deep powder snow?
3) When I get back to my truck I seal my camera and lens in a large Ziploc style plastic bag. The odor-proof plastic bear bags from REI are perfect for this. Then, if I am moving to a new location, I put the bag on my dashboard where the defroster can blast it. If I am staying put I put the bag in front of the furnace in my camper. Obviously I don't open the bag until the contents are warm, to avoid condensation.
4) Usually when it is snowing, everything is cold enough that the snow is not a problem because it just falls off the camera like feathers. If it is wet snow or rain, then I use a StormJacket. If I'm using a tripod then a great setup (if it's not windy) is to throw a poncho over the whole affair and get under it without poking your head through the head hole - that's where the lens goes.
5) Lastly, if you are really new to this and just venturing out...
Skis are much faster and far more efficient to travel on, but require more skill than showshoes and are harder to deal with while photographing. First of all you now have ski poles to deal with, in addition to a tripod, camera, etc. Also, it is more tiring to stay balanced on skis for long periods of time and lastly, skis love to collide with tripod legs when you need to move around. Bottom line, a pair of technical snowshoes (MSR Lightning Ascent) are far easier to deal with than skis. They are smaller and lighter than standard snowshoes and will grip on icy slopes as well. They are so convenient that I have tied them on my pack for an all-day or multi-day trip. Then when I get to the area where I want to work, I ditch the skis and poles and put on the snowshoes. I see a lot of people snowshoeing with ski poles, but if you are reasonably athletic you can easily do without. Eliminate the clutter.