Photographing in Yellowstone's winter can be a tricky venture.  My preferred time to photograph, whether it be in Yellowstone's geyser basins or in wildlife rich Lamar Valley, is on morning's where the thermometer dips well into the negatives, in farenheit.  Often, when the thermostat dips below minus 20 or colder, I look like I do in the image below. 

It may look cold, and it is... in that image, it was about minus 22 F (-29C), but with the right gear, it's possible to stay warm.  I typically layer with two pairs of insulated under garments, both top and bottom.  I then use a pair of liner socks, a pair of heavy socks, and a pair of snow boots.  I also wear a pair of moisture and wind resistant pants, a fleece vest, and a winter jacket.  For my neck and head, I'll wear a balaclava and then a knit hat and possibly the hood from my jacket.  For my hands, I have a pair of silk liner gloves, a pair of fleece fingerless gloves, and then a pair of insulated mitts.  The liner gloves and fingerless gloves allow me to operate my camera while still staying somewhat warm, and when I'm not shooting, the outer mitts keep my hands toasty warm. 

I've read alot about what to do and not to do with your camera in extreme cold conditions, but I've found my camera tends to deal with the cold just fine.  I always carry plenty of spare batteries and keep them inside my jacket.  Batteries don't last long in very cold temperatures.  However, aside from the batteries, my cameras usually hold up without problems.  It's not uncommon for the rear LCD to frost over to the point I can't see it, or it can get sluggish due to the cold, but I've never had any real problems.  I do try to not change lenses unless I absolutely have to, but I usually carry two cameras with zoom lenses attached, so there's no need to switch out lenses. 

All the images here were taken when the temperatures were below minus 20 F.  The above image is the black and white "companion" image of this week's Photo of the Week.  I really liked the symmetry of the two bison in this shot but ultimately, I preferred the turned head of the other shot seen here.  With a little preparation, it's possible to stay warm, safe, and still come away with some nice images during winter's cold.