Boots: One of the most important pieces of gear you'll need is a warm pair of boots. There is much debate over just what type of boot is best and much of it once again comes back to the type of hike you'll be doing and the type of person you are. There are several options and here they are in no particular order.
First is to winter hike in regular summer weight hiking boots. I know that many think this type of boot doesn't provide enough warmth but I also know that I've used them and know of dozens of others that have also. Now, if you your summer "boots" are a lightweight, low, fabric type then I am by no means saying that they will do. For years I used a pair of all leather mid to heavy weight summer back packing boots for winter hiking. It's important to note that they were purchased in a size large enough to allow me to wear a liner sock, a vapor barrier sock and then a very heavy wool sock. They kept my feet warm and toasty on every hike I did as long as the temps were not below zero. If they were, I simply didn't hike that day.
Second is to use a "pac" type of boot like a pair of Sorels. I do know people that use these and I have seen them on the trail on occasion but I personally prefer something with more support. I don't think my feet could walk all day in a boot that's as loose and floppy on my foot as these types of boots are. But, if you're doing shorter hikes or your feet are not like mine then these may work fine for you. You can certainly buy them that are rated to temperatures much lower than anything you may encounter in the average New England winter.
Third is an all leather insulated hiking boot. These are becoming more and more popular as many people discover them and find that they can be much more comfortable than a plastic boot and fit much better than a "pac" boot. They don't have nearly the insulation but that can be over come in other ways and if you're going to be hiking up a mountain you will most likely not want a boot that's rated for 100 below anyway. This has become my boot of choice and I've tried probably a dozen different boots and boot combinations over the years. Many find that the biggest obstacle to using this type of boots it their price. They can often be $250 to $400 but if you shop wisely you can do much better.
Fourth is a plastic double boot. For those unfamiliar with this type of boot think of a ski boot. Well it's not exactly the same it is a rigid plastic shell with a softer, removable inner bootie. If you're doing any serious alpine mountaineering, going out for longer than a day hike, ice climbing or just tend to have very cold feet then these may be the boot for you.
Base Layer: In winter as in any season the best way to stay comfortable is to use a layering system rather than to try to stay warm with one big heavy jacket. As you hike more in winter you'll learn that staying cool is more of a challenge than staying warm! If all you've got is that big arctic down jacket you'll be nice and toasty when you start up the trail but in no time at all, especially if you're snowshoeing and carrying a heavy pack you'll be much, much too warm. Then you begin to perspire, get damp and then come time to stop for a break you'll be freezing in no time at all. So I start with a pair of long underwear made of one of the many modern synthetic fabrics. An important point to note here is that you should really try to avoid cotton clothes of any type when winter hiking. There's an old mountaineering adage that says, "Cotton kills!" Cotton loses nearly all it's insulating qualities when wet. Where as fleece or wool will insulate even if wet. If you don't have, don't like, or simply can't afford fleece then don't forget that wool is what was used for years and will keep you warm even when wet. The big advantage of the newer synthetic fabrics is that they not only insulate even when wet but they dry astoundingly rapidly! For me, it's impossible to not sweat while hiking and these types of fabrics dry amazingly quickly so even if I'm cold all I have to do is to slow down for 20 or 30 minutes to the point where I'm not sweating and in that amount of time the base layer is nearly dry! Up top I generally wear a synthetic T Shirt and over that I wear a long sleeve zip turtle neck shirt of the same fabric. That way I can vent the turtle neck and if I really start over heating I can strip down to just the T Shirt. Yep, it's true, it's not uncommon to be climbing up a trail on a winter's day and see people in T Shirts and even shorts!
Insulating Or Middle Layer: Again this one varies depending on the temps and just what you're doing but you will want at least one layer of fleece and perhaps more. What I do once the T Shirt and Turtle Neck aren't enough to keep me warm is put on a mid weight fleece vest. That generally does the trick in all but the coldest conditions or when I'm stopped. If not, I also carry a mid weight fleece jacket. For those times that I'm at rest, or for an emergency I also carry mid weight down jacket if I'm going to be out for long, am going very far, or if I'm venturing above the treeline.
Wind/Rain Or Outer Layer: On top of what ever you need to keep you warm you will often need some type of wind and/or water proof layer. In winter this will be worn much more for it's wind shedding qualities than for it's waterproofness. Especially if venturing above treeline, as it's there that you'll find that the wind is seldom still in the winter! The big question is, is it necessary to buy the modern, high tech, waterproof/breathable fabrics or not. Unfortunately, once again, there is no set in stone answer here. If you are the type that tends to sweat very little in winter than I would say, no you don't need to spend the extra money on the high tech fabrics. Of course on the other extreme, you may sweat like I do in winter, profusely! In that case you'll want every advantage you can get to help rid yourself of perspiration when the winds force you to wear some type of shell layer. Personally I DO use a waterproof/breathable shell BUT I want to make sure to make it known that there is no way that it "breathes" nearly enough to keep me dry! The only solution for folks like me is to avoid putting the shell on until it is positively necessary! A very handy feature to look for when purchasing pants is that they have zippers that run the full length of both legs. This makes it much easier to put them on without having to remove your boots etc.
Head Wear: I called it head wear because there is such a diversity of products out there to wear on your head that it's not adequate to refer to the entire group simply as hats anymore. What I find works best is to have some type of lighter hat for the times when you're climbing or the temps are high. Some people use a simple headband in this instance. Then you'll want a good heavy hat of either fleece or wool that covers your ears well. And, for those really cold and/or windy times you'll want something like a balaclava. If you don't go the balaclava route than you can use your hat with a simple inexpensive face mask but it is important that you be able to cover every inch of exposed flesh if the temps get too low. When the temps are below zero and there's a wind it's quite possible for exposed flesh to freeze in as little as a minute or two! Yes, that's what I said, freeze! Frostbite can happen just that fast!
Mittens/Gloves Personally I seldom wear gloves other than as a base layer. By wearing a thin "liner" glove you can avoid ever having to expose bare skin. Even if you must take off your mittens you still have something to protect your hands and to keep them from freezing to steel crampons or snowshoes. You should most likely have at least a couple of pairs of liner gloves, a pair or two of good warm fleece or wool mittens and a pair of shell mitts to cover everything and keep the mittens etc. dry. If the trees, branches and everything else is snow covered it's important to either make a conscious effort to not grab things to pull yourself along etc. unless you put on the shell mitts right away. It takes very little time to end up with soaking wet mittens that become very cold, very quickly!