I fish the park in winter a lot. I certainly don't catch as many fish as I do other times of the year, but the atmosphere within the park is very relaxing. Peaceful to be exact.
It is one of the only times of the year I actually enjoy fishing Tremont. That is if they have the road closed.
If the roads are not closed, I enjoy fishing the "easier to get to" brook trout streams. This is contradictory to what most people say about staying low in elevation, but the brookies seem to stay hungry all the time.
I also have better luck fishing the smaller streams and staying away from the larger waters. This could be due to the density of trout in the smaller streams. If I drift my fly over/around 100 trout, I'm more likely to attract the interest of one than if I drifted my fly by 10 trout.
I catch a surprising number of fish on a dry fly. I always start with a dry/dropper combo and on some trips I'm amazed at the number of rises I get on the dry. If you are getting refusals on the dry, cut the dropper off to get a better drift. Also, keep some BWO's on hand. Sometimes you'll catch a good hatch and be able to fish to rising fish.
Fishing is almost always better in the afternoons when the water warms some. But, sometimes the fish forget that so don't stay home if you only have mornings to fish. My best winter day came on a cold, dreary, cloudy winter morning about 2 years ago. I fished above Tremont, in the snow, and caught fish on an orange EHC all morning long.