I'm a tour guide out of Phoenix and I've been to the Grand Canyon over 400 times.
Winter time in the Grand Canyon is cold, but dramatic. Most of the time, the roads are clear except right after a storm. Sometimes there's patches of ice inside the park (they can be a little slow plowing them), but the roads to the park are normally cleared quickly.
The park gets very crowded in the summertime when the kids are out of school. Winter is better if you don't like crowds (and don't mind the cold).
If you don't want to do the driving, I do suggest a tour company, but stay with the small companies that use vans rather than busses. You will get a more intimate tour that way.
There's a free ebook on touring arizona (including The Grand Canyon) at http://doingaz.com
Hope this helps.
It was warm and sunny when we left Las Vegas in the morning. I almost didn't wear a coat, but I'm glad I did. It gets really, really cold in the canyon. I guess that may be obvious, but I wasn't thinking. We spent all day getting on and off the bus, doing a lot of walking and standing outside. At points I was so cold I almost wasn't able to enjoy it. Later in the day it actually started snowing and the wind was really strong. I wished I had dressed warmer. Bring a scarf and gloves if you go.
Fondest memory: The views were absolutely amazing! I'm sure everyone has seen pictures, but there's nothing like seeing it for yourself. The colors are beautiful. I couldn't believe how mysteriously enchanting it was.
If you are planning a trip to the Grand Canyon, don't worry about the weather. First of all, given that you're in a desert, it's unlikely that you're entire visit will be spoiled by rain unless you've only budgetted an hour or two (then shame on you!). Secondly, the canyon's moods change with the weather and clouds, snow and rain showers can help you create spectacular pictures! We would love to see the Grand Canyon in a snowstorm or during a thunderstorm!
In fact, the worst weather is probably clear, hot and dry because that can be lethal to hikers. Rain in the desert is a thirst quencher, not something to worry about!
Favorite thing: If you are there in the winter, then you can make snowballs and throw them in the air just like us on the left!!!!