GoreTex "extreme wet weather" rated outerwear, and silk underwear, are a good start to keeping warm and dry in the worst wx. Silk liners won't itch like wool can, and they keep you warm even when damp, just as well as the new synthetics do. With wool, silk, polartec, and the like, it is no longer hard to keep warm, even if you get a bit damp around the edges.
Once you figure out how to stay warm and dry, the rest can be fun because there's always good wind in bad weather.
The rest depends on how or if you like it. Some folks use ski goggles in driving rain, some use a towel or scarf around their neck and a hat instead of a hood. Lightweight neoprene diving gloves (the thin ones) make a great way to keep some finger dexterity while keeping the fingers warm, too.
And of course, the big crowds just aren't out there.