I'll start off by saying that, although I do all my hiking east of the Mississippi and have done a fair amount of winter camping with Scout troops, little of my experience has been in the mountains, and none has been in the mountains when there was significant snow or temperatures below 20 degrees.

Accordingly, I'd only have a couple of general comments.

First, I would think you should avoid canister stoves; after one cold-weather experience with a canister stove, I now choose a white gas stove when the temperatures dip below freezing. Others have told me their canister stoves work fine into the mid-teens, and I have no reason to doubt them. My only experience with a canister stove in cold was with a Jetboil PCS, when the temperature was about 20; I had to hold the canister in my hands to get it to work well. (The Jetboil's pot locks onto the stove, which makes this feasible; I wouldn't try it otherwise.) A friend told me he got his Jetboil to work at 10 degrees by heating a cup of water with the feeble little flame, then setting the canister in the cup; at that point the canister warmed enough to function at near-normal levels.

Another general comment would be to make sure that, in addition to a reliable, accurately-rated sleeping bag, be sure to take enough sleeping pad to adequately insulate you from the ground. Around here (Ohio, Kentucky, Indiana flatlands), my Prolite Plus pad has always been enough. I did have problems with a Big Agnes Insulated Air Core pad letting a chill through at 25 degrees; others have reported similar issues with NeoAir pads at even higher temperatures. Many winter campers will take along a closed-cell foam pad to place under or over (opinions vary) their regular pad to boost its insulating ability. (Such a pad is also handy to sit on at lunch or in camp.)

Don't fill your water bottles completely full. That way, if they freeze, they won't burst. Also, store them upside down in the tent; if they don't freeze solid, the water won't be blocking the mouth of the bottle. Also, try to insulate the bottle if you can: put it inside your sleeping bag, or consider using an insulated container (I think OR and Granite Gear both make them, or you can make one out of an old closed-cell foam pad.) Others can tell you what effect the cold has on filters; I don't have much experience below freezing, so can't comment intelligently.

"Warm enough" clothes and footwear are a given; I don't have the experience to presume to tell you what you'll need in the eastern mountains - others will have that knowledge. I would recommend that you take one or two more pairs of socks than you normally would; cold, wet feet are both horrible and dangerous.

Finally, I'd recommend that you build a safety margin into your gear kit. For me, in the flatlands, it works like this: My sleeping bag is rated to 20 degrees (conservatively, since it's a Western Mountaineering bag.) So, that's the coldest predicted lows I'll go out into. However, I'll also have down booties, down pants, hooded down sweater-jacket and down mittens to wear over my midweight wool longjohns, plus I can put on my rain suit, balaclava, stocking cap, and liner gloves if I need to. My sleeping bag has enough room in it that I can wear those garments inside the bag without compressing any insulation. So, if the lows unexpectedly drop below the projected 20 I'm planning for, I figure I'm OK to around 10 or maybe even 5 - which means a 10 or 15 degree safety margin.

As I said, this is intended as very general advice, a starting place from someone with limited experience in the conditions you describe. There are many others here who can give you much more well-informed and specific advice.