I've been dreaming about a winter trip to Yellowstone for years but haven't made the jump yet. I have the park webcams at the top of my bookmarks list and check them daily. The full-moon times in winter are best. Last week I saw the first skiers I've seen there this winter - might have been you guys!
An XC trip to Lone Star sounds great. I love searching for backcountry thermal areas on google maps. Regarding batteries, I've been doing some backyard astrophotography lately and the cold is really doing a number on the camera batteries (and my toes). The Li-ions seem to be particularly susceptible. I've taken to bringing them inside periodically to warm by the stove. When your batts are low you might be able to squeeze one or two more shots out of them by putting them in a pocket or armpit to warm up. Maybe you're already doing that.
The li-ion batteries in my headlamp died during the Tunnel Hill 100 because of cold. Fortunately, it was a full moon, so I didn't really need a light.
I think most of my battery problem was that I hadn't charged it recently but had used it a bunch.
I highly recommend a winter visit to Yellowstone. Mary and I have been there 8 times in the winter. The scenery is really spectacular with snow. It is a bit easier to see many of the animals. The bears are usually hibernating, so no stress about bumping into a hungry grizzly. It is also fun to see all of the tracks in the snow.
A big advantage of winter is the lack of crowds. I check the web cam most days and during the normal season, there's a pretty big crowd at Old Faithful. In the winter you can be there alone. That's pretty sweet.
The easiest way to visit in the winter is to fly to Bozeman, rent a car, and hang out in the north part of the park. The road from Gardiner to Cooke City is open year round. Time permitting, getting a snow coach into the interior of the park is great.
In the winter we see lots of small group tours. A lot of the tours are serious photographers - getting out to the Lamar Valley before the sun rises and carrying monster lenses.