MHobbs,
Great question which will spur a variety of answers. Here's my take.
BOOTS - I think there are 3 basic solutions. 1) Plastic double boots with removable liners. 2) Sorel-style pac boots with removable liners. 3) Single leather boots with insulated full coverage gaitors and VB socks. Plastic double boots are the most common for good reason. They are supportive provide a solid grip in snow and work well with crampons (something you will need too) and are very warm. They are generally easy to deal to with logistically. On the downside, they can be rough on your feet if you hike on rock or dirt instead of snow. Sorel-style pac boots are a reasonable alternative. They don't provide good support and you have to use strap-on crampons. But they are warm. Very few people will argue these points.
Adding insulated gaitors (MEC still sells them) adds a significant amount of warmth to leather boots. This is very fiddly and generally requires that you reglue them on every season with Shoe Goo. Many people will argue this is not warm enough to be safe. As a Nordic skier who is forced to go this route with his ski boots, I feel safe down to about -10F using this approach. This brings up a larger point...
IMO, my suggestion is to think about boot warmth holistically and to consider all of your gear collectively to arrive at a go/no-go bottom temperature below which you will leave the woods. For me, this is -10F. I will simply pull the plug on a trip if there is a reasonable chance I will face temperatures below this. Nearly all of my gear starts to become inadequate at that point. Boots, yes. Also sleeping bag, mittens, possibly stove and so on. I've been to -15F on numerous occasions and know I can (or used to be able to) operate at that temp, but I now draw the safety line above that at -10F. I've pissed of good friends refusing to go on trips but I've never had black toes either and know people who have (they were wearing plastic double boots, temps were in the -15F to -20F range with high winds).
Getting back to the question of leather boots and insulated gaitors, I feel comfortable with this combination down to -10F. One modification is that I also use VB socks between my liner sock and wools socks at about 10F. This keeps my socks and boots dry from sweat and thus much warmer. An essential part of the system, imo.
SNOWSHOES - In the Whites, I think the decisions about snowshoes depends on your hiking goals. If you are limiting your winter hikes to places that receive a lot of traffic, then crampons are more important. I'm thinking here of things like Carter Notch via 19 Mile Brook, Hermit Lake via Lower Tuckerman Ravine. Crag Camp via Amphibrach and Spur. Grey Knob via Lowes. Crawford Path. Lafayette via Old Bridal Path. IME, the reality is that 9 days out of 10, snowshoes will not help on high traffic trails but crampons are essential. Yes, just after a deep snow, you need snowshoes. And in the spring when things go corn, you need them to prevent post-holing. But generally, crampons are much more essential.
As an aside, I suggest to new winter hikers that that they stick to well traveled routes, to increase the odds that somebody can provide aid should things go bad. But, that's a highly personal decision.
If you set your sights to less traveled locations, snow shoes or skis become essential for forward motion. Slogging sucks. But then, as a skier, I think snow shoeing sucks compared to skiing. Another reason I don't own them. If there's enough snow to need them, I'm skiing instead!!!
BTW, as a XC skier, I'm pretty ambivalent about the snowshoe vs post-holing debate. IMO, when I take skis onto a hiking trail, I recognize I'm entering a multi-use situation and as a result, I have no expectations. In fact, if the trail is remotely close enough to a road that hiker can get to it, I just expect that the hikers will destroy the trail for skiing. Boots, post-holes and snowshoes all drive the trails to a trench and the USFS and other land managers don't provide good signage telling people to stay out of ski tracks and even when they do (Greeley Ponds, Lincoln Woods area) the signs get ignored and it just doesn't matter because a few miles in, trails get so narrow that shared use means 1 trench any how.
Now... If I wanted to be snarky, I would suggest that a lot of the snowshoe zeal comes from people who suffer while carrying the heavy, underused and joyless things on their backs and since misery loves company, they want to ensure that everybody else hiking along trenched out trails while wearing crampons are also carrying the same heavy, underused and joyless snow shoes. My suggestion is to get some skis. When you ski fast enough, the crunch, crunch, crunch of sullen snowshoers creates the coolest Doppler effect!!! But, I really promised I wouldn't be snarky today so I won't say that. (ahem)
In all seriousness, if you're heading to places that aren't trenched out, IMO you really need crampons plus either snowshoes or skis.