A few words of advice for beginner winter hikers: DON'T GO FOR THE SUMMIT!! Even if you are an experienced summer hiker on Mount Washington, the mountain in winter is a very different place. Normal winter weather on the mountain is much colder and much windier than in summer, requiring lots of warm clothing and windgear (including insulated boots, face mask, and goggles). Of course, it tends to be very snowy, too, so snowshoes (and familiarity with their use) may be needed, especially for the approaches below treeline. Trail finding, especially in stormy conditions above treeline, can be very, very difficult. Steep (sometimes icy) snowslopes require ice axe and crampons, and the ability to use them which comes from training and practice. Don't underestimate the danger in traveling on steep slopes of snow or ice - there have been several fatalities on the mountain because of slips and falls in such areas. A number of slopes on the mountain (including those commonly ascended on trips to the summit) are prone to avalanche - a hazard which has accounted for several fatal accidents on the mountain.

In short, the steep slopes and high open areas on the mountain are no place for a beginner winter hiker. With proper precautions to protect against cold (and its attendant risks of hypothermia and frostbite), novice winter hikers can explore the mountain's lower slopes. The Tuckerman Ravine Trail is usually well-packed from the A.M.C. Pinkham Notch Visitor Center to the Hermit Lake Shelter Area, and is a fine place to start winter familiarity with the mountain. Weather permitting, there are fine views up toward the Tuckerman Ravine Headwall from Hermit Lake.
Snowshoes are usually not needed for the 2.4 miles from Pinkham Notch to Hermit Lake, as this part of the Trail tends to be well-packed by foot traffic and by the U.S. Forest Service snow tractor which the Snow Rangers use on their near daily visits to assess avalanche hazard in Tuckerman and Huntington Ravines and adjacent areas. (On some occasions immediately after storms, snowshoes may be helpful.) Especially early and late in the season, crampons or similar aids to traction may be helpful, even on this section of the Trail, to allow easy walking on icy or very hard-packed areas, though the crampon-less hiker has an easy alternative when the going gets too tough - turn back down the trail and come back when conditions are more cooperative!
Attention must be paid to having enough warm clothing and windgear - though this section of the Trail is entirely below treeline, strong winds can penetrate the forest and have a really chilling impact on hikers. Additionally, other hiking equipment and supplies should be carried as any responsible hiker would have for a summer outing, such as food, water (insulated to protect from freezing - a thermos full of a hot drink may be much appreciated), a map, a compass, a flashlight (remember that batteries can be adversely affected by cold weather), personal medications (properly stored - those that are affected by cold might need special packing), a basic first aid and repair kit, and spare eyeglasses. Sunglasses and sunblock might also be brought along, especially in late winter. A ski pole, or ski poles, can be handy to have along. Basic emergency shelter, such as a plastic tarp, should also be carried; a group might wish to bring along a sleeping bag and an insulating pad as extra emergency items.
Some clothing which you should consider bringing along, even on a relatively modest winter hike such as this one, includes:
For toting all this gear, plus the clothes you have with you but aren't wearing at the moment, you'll need a pack, and probably a bigger one than you bring on your summer dayhikes.
Please note that most climbers think synthetic fabrics are best for clothing because the synthetics continue to provide some insulating value even when slightly damp by snow, fog, rain, or perspiration. (Try really hard to keep you clothing as dry as possible all the same.) Wool is a natural alternate fabric, but most climbers judge that it does not perform as well as current synthetics, as it generally absorbs more moisture and takes longer to dry when dampened. Cotton is to be avoided - when damp, it speeds cooling and can be deadly. There is no place for jeans, cotton corduroys, chamois shirts, cotton flannels, cotton waffle underwear, or cotton sweatshirts on Mount Washington in winter!
The more adventurous can consult with the A.M.C. Hermit Lake caretaker or the U.S.F.S. Snow Rangers and can consider a trip toward the base of Tuckerman or Huntington Ravines, if avalanche hazard is low. Be aware that "low" hazard does not mean "no" hazard, so stay off of and away from steep and open slopes - enjoy the views of them from a safe distance. Remember that it's not only high-angle climbers and skiers who have perished in Mount Washington avalanches - at least one casual hiker was killed by an avalanche as he strolled near the base of the Tuckerman Headwall.
There are other snowshoe excursions on the lower slopes of the mountain that can be considered by a party of less experienced winter hikers. Any can provide an introduction to some of the challenges of winter trail-finding (when the footway is covered and, with deep snow, any paint blazes on trees may be hidden, too) and to the difficulties of packing trail and of ascending and descending steep slopes on snowshoes. Among the trails that could be considered are the Boott Spur Trail (only to treeline!) or Glen Boulder Trail (only to treeline!) or the Raymond Path. The Old Jackson Road is often traveled by cross-country skiers, but that can give access to the Madison Gulf Trail which leads to a viewpoint at Low's Bald Spot.
Hikers familiar with the mountain in summer might ask, "What about the Ammonoosuc Ravine Trail or Jewell Trail? Couldn't we try them on snowshoes to treeline?" In the distant past, these trails were only lightly used in winter, as there was no public vehicular access to the western base of the mountain. Since the winter of 2004-2005, the Base Road to the Cog Railway has been plowed and open to the public. Note that the U.S. Forest Service parking lot at the summer trailhead for these trails is not plowed, so that hikers using these trails in winter typically park at the private parking lot at the Cog Railway base station (a significant courtesy granted by the Cog to hikers). Be aware that hikers on the western side of the mountain do not have access to any public facilities at the Cog Railway base (no restrooms, no visitor center), nor do they have facilities higher up on the mountain. (In these respects, the western side is unlike the eastern side, with facilities at Pinkham Notch and at Hermit Lake.) In ideal conditions, the Jewell Trail can be a pleasant ascent to treeline for an experienced snowshoer. The Ammonoosuc Ravine Trail is very steep after Gem Pool, and can be very obscure higher up in the Ravine.
Check the Backcountry Weather and Trails Conditions page and the latest USFS Avalanche Bulletin to determine what conditions you might encounter before going on a winter hike.