The big problem with the 400 5.6 is no IS. Are you using a tripod? A good tripod with ball head? If not, be wary of the 400 5.6. The 70-300 is an incredibly useful lens. I used to have the old 70-300 IS not L, and it was the best lens ever! (not as good as my 70-200 2.8, but do understand my meaning here...)
What kind of animals are you trying to get pictures of? And how many animals are out and about in yellowstone in the winter? Some, indeed, but perhaps they might be rather remote...