Lots of great ideas! I am far from an experienced winter hiker, but I have dabbled in the easy, and more difficult treks. Here is what I have learned on the higer peaks.
1) Mt Pierce: My first winter 4K. Crawford Path is nice and usually broken out. Just be careful if there is a blizzard with strong winds. It is easy to go the wrong way when heading back to the Crawford Path after summiting.
2) Tecumseh: My 2nd winter 4K..Keep an eye on skiers! Sometimes they will use the hiking trail instead, and you need to get the heck out of the way in a split seconds notice. There is a thread about my experience somewhere.
3) Lafayette-Don't try to break trail if you aren't ready for it. A few friends and myself tried the Laf via Skookumchuck and then lost the trail easily. Also-the Old Bridle Path is a great trek up to the hut. There are some steep spots (esp the agonies) but its a gorgeous trail up to the hut. After that things can get dicey, and WATCH OUT for spruce traps! Learned that one the hard way....ooh, and make sure you always stay together.
4)Moosilauke-Glencliff is a great trail to follow because you are protected, UNTIL treeline. Then it can get dicey. I had to turn around less than 1/4 mile from the summit due to near zero visib, and 50+ mph winds (I have an anemometer to prove this) While I havent done it in winter, I think Gorge Brook Tr is a better idea because you are protected from the NW winds till pretty much the summit. Just know that you will have about a 1.6 mi roadwalk each way.
5) Carter Dome...I failed this one miserably because I wanted to hit up the hut first and then go up the super steep AT to the summit. Bad idea...go the opposite way. My snowshoes were not gripping and I was sliding more than climbing, which is incredibly demoralizing, and not worth the struggle.
Also, while you may be in the woods most of the way, zero degrees is still zero degrees...COLD. Dress appropriately. Plus, when it gets that cold, it can be difficult to breathe. Finally, make sure you stay hydrated, and properly nourished. It is very easy to fail at this because you don't think you are thirty because you might not sweat as much in winter. But really, you still might be dehydrated.
Now to the positive: I've learned about my limits over the years, and I now know what I am comfortable with doing. Plus, I consider winter to be the most gorgeous time of year to hike. The air is clean and clear and visibility can be 100 miles or more on the higher peaks. There are no bugs and few if any rocks to get in your way. People I've met on trail in the winter tend to be much happer, and friendlier, and helpful than in summer. I think that is because they tend to be more experienced than some of the weekend hikers you meet during the warmer months.
Those are my experiences.