Did Washington a few weeks ago (1/24) via Jewell, and parked in the 3 level at the Cog (asked an RR employee if we needed to pay anything - said no). Jewell doesn't get quite as much traffic as Lions Head, but since it hadn't snowed in awhile, we just took crampons and poles. After the intersection just above Clay (about a mile from the summit) consider crossing the tracks and keeping them between you and the Great Gulf.
As for what to make sure you bring - full winter gear, including face mask and warm mitts.
I like doing Washington from either side, but am finding I like the Cog side better now that the road is open as 1) more above treeline time (just be sure to pick your day), 2) not quite as steep. I don't mind steep on the ascent, but it gets old on the descent, and 3) can rather easily include Monroe if it's a good day and the spirit moves.