Mt. Washington is as beautiful as ever, now that its upper realms are home to over a meter of snow. M. and I took the winter route up to the summit, and were fortunate enough to have dry weather and some views until we got near the top, when it started snowing.
The current conditions are: wet and slightly slippery trail for the first mile, and patches of snow for the second. From the Owl Lookout, the snow deepens, although you don't need snowshoes. There are a lot of water features in the half mile or so from the lookout to the major creek crossing. At that point, you head uphill and the snow gets pretty deep, and snowshoes would still be optional since the snow provides pretty good traction here.
Once you get to the ponds, snowshoes become almost necessary. We took the slightly steeper and shorter winter route to the west, but plenty of people were taking the summer route...the trail is very obvious the whole way (although it's been snowing). The winter route has a couple of very steep parts that aren't easy, but they're short. Eventually, you connect up with the summer route, then it's no more than half a mile to the top.
This is a fantastic hike at different times of year, and in addition to the summer and winter routes, you can go the back way around Change Peak, although that trail is probably hard to follow right now (see my trip report from earlier this year for details). Mt. Washington is peaceful since it's not as popular as other nearby hikes, but it's very accessible, being just off of I-90.
Directions: from Seattle, take exit 38 on I-90, turn right at the bottom, immediately cross over a small bridge and turn right into the parking lot. The trail head is clearly marked with two large rocks. Climb up a steep, short path to reach a road, and climb up that a short distance to connect with the John Wayne Trail. Continue west about two minutes until you see a trail heading off to the left...this is easy to miss: it's flanked by two small trees and descends a couple of steps from the trail initially.
The Mt. WA trail starts climbing immediately. After about 1.5 miles, there's a fork...follow the small sign and stay right for Mt. Washington. After about 2 (total) miles, you're at the Owl Lookout. After another half mile or so, the Change Peak trail splits off to the left...this is clearly marked. A little further on and you'll cross the big creek. After another 15 minutes or so, you enter a meadow/valley with several very wet creek crossings, then climb another 10 minutes to the ponds. Here's where you can elect to go left (east) to follow the summer route, or right to take the winter route.
Hiking at a decent pace with only a few short breaks, it took us just shy of 3 hours to go up, and just shy of 2 to descend the same way. The snow gave way to freezing rain for the last 20 or 30 minutes, but otherwise it was gorgeous.