I'm a big fan of hiking in the snow. It has its challenges, like not being able to see what's under the snow, for instance. But it's rare to see anyone else out in it and the dogs seem to love it as much as I do. For a time, a friend of mine and I would literally load up our dogs and gear to travel virtually anywhere east of the Mississippi chasing big snows to hike in (having a Subaru helps a great deal!!!). We ended up in West Virginia during a 10" snowfall. The flakes were the size of cocktail napkins as we made our way thru the woods on logging/fire roads.
If you can get to and from the trailhead safely, by all means get out and try it! The cold doesn't last long once you get moving, but I highly recommend some essential gear: warm boots (they should have a quality sole, be waterproof, as well as toasty warm), mittens (forget the gloves, you don't need fingers to hike), a waterproof shell, a down layer, ski pants or layers, and your favorite winter hat (don't forget a light source- just in case). If you're traveling unfamiliar territory, it's probably best to stay on fire/logging roads, as trails can quickly become unrecognizeable in heavy snow. Also keep in mind that hiking in snow, for several reasons, requires a lot more energy. So don't get carried away with your mileage expectations.
I just thoroughly enjoy hiking in a snow covered woods with its depth-of-field viewing and the quiet thump of flakes hitting the ground. Get out and have a look around. Don't forget to sit and watch. Sometimes it's ok to watch the world go by!