Here are some photos taken on a hike up Lion's Head:
http://outdoors.webshots.com/album/228158607ptuljl
NB: No pictures from the summit. My camera froze up. Be sure the batteries in your camera are Lithium
Be sure your mittens are secured with a wrist strap in case you have to remove them, for example, to adjust a strap or crampon. Removed gloves placed on the ground have been known to have been blown away, including a hiker who lost his life, slipping over a ledge while chasing a glove being blown away along the ground.
Take a bivy sack. I know of someone who was caught in a storm on Washington and had to spend the night who saved herself because she had a bivy. Another less prepared day hiker lost her life in the same storm on another nearby mountain.
Take crampons. Even on packed snow, crampons will give you improved traction. Above Tukermans' ravine, ice is the norm. Wind blown snow will most likely be crusty, too.
Sure you can hike it in low cuts, but don't do it in winter. You are asking for frosbite or at least freezing toes. If for any reason you have to stand or stay in one spot for a while, you definitely want insulated boots. I know many hike in New England winters without insulated boots, but….
You do not need plastic mountaineering boots if you do not have them, but other models of insulated boots are not expensive and many are not heavy. Make sure you can fit crampons on them, however. For example, I have seen Baffin Boots reviewed at this site.
You can rent plastic boots from EMS, or Wilderness Mountaineering right in North Conway only a few miles from Mt. Washington. They are comfortable and a luxury. They are perfect for a Mt. Washington hike.
Wearing crampons, you will find that the heavier gaiters might more durable to resist tearing. Crampons often rip gaiters.
Face mask and ski googles?
Small head lamp with lithium batteries.
Have a turn around time and stick to it regardless of where you are on your hike. January days are short!
BTW those photos were taken on a cloudless windless day on the mountain a day after a fresh December snowfall. Beautiful!
Next time I tried hiking Washington in winter it was 17 below zero and howling winds at the Hermit Lake shelter where we spent the night. So, that is as far as we got, but the days were cloudless and we still had fun!
On winter hikes I put liner gloves on at the trailhead and never take them off. I have not had frostbitten fingers in awhile now.