Having taken dozens of backpacking trips between 1987 and 2001 all over the Whites (I became addicted to remote bushwhack ponds rather than trail hikes) I can offer that, unless you REALLY like tough winter climbs, and are experienced and prepared, you are better holding off until early June...even a little later on Mt. Washington where there's often skiing until then. Especially if you are a novice or are planning "simply" a day hike, since you should prepare for Washington's worst in any month of the year. Even climbing 4000 footers, I sometimes ran into snow packed trails on Memorial Day weekends.
The "walk" up Washington via Tuckerman's Ravine is supposed to be one of the easier routes, although I've never gone up that way. The trail that starts up from the West near the Cog Rail Station (Ammonoosuc Ravine Trail) is not too bad (unless you're packin' 60 lbs. as I was). It's pretty much a busy "highway" that comes out of the forest near the Lakes of the Clouds hut, and then is another 1.5 miles of exposed rocky trail to the top...often in fog so thick it's hard to stay on the trail! There's a way to make that trip a big loop, but it would be a loooong, exhausting day. I overnighted in the hut's lower bunkroom ($5 then), went to the summit the next day, and then down the north headwall (in a raging ice storm in July) to camp in the Great Gulf. Next day it was up over Mt. Jefferson and out.
The Great Gulf is another spectacular way to come in, but it would be best to plan a multi-day camping trek. That time our family (see photo below of us climbing the headwall) hit 75mph winds and 50 degrees in pea soup at the top. Then, 1/2 hour later the fog blew away, the wind died down, it became a sunny 70 degrees...and I could see FOREVER!
The area is laced with SO many trails and has SO many possibilities that there is something for (almost) everybody's level of experience. Looking at one of your web site references that gives distances and time for popular options, just because you MIGHT be able to do the distance in the time listed doesn't mean you WANT to. I'd figure on at LEAST half again as much time to stop and gander at the scenery, take pictures, catch a bite to eat at the top and do a little sight seeing before starting back down in plenty of daylight. You DON'T want to travel some of those steep, rocky, rooty trails at night!. Keep the early adventures simple, fun... and safe!
And, send me a postcard. (Actually you CAN from the Mt. Washington Post Office.)
It's currently -25 C wind chill factor, with wind gusts of 82 mph.)
