"How can I learn to transition to winter hiking and camping? ..."
Buy a good sleeping bag. :)
Along with Jims advice, you could read some books, definitely look at gear lists from locals, or take a course.
An example of how I started...I probably spent a few months trolling for information and accumulating gear. Then one day, I just went to my local park and hiked in about 1 hour. Set up camp, ate some dinner, and went to bed. It droppped to -15*C that night and I survived.
It was that first trip that I found out upright canister stoves don't work very well in cold temps, and you need more pad then a ridgerest to stay warm. I also tried to melt snow in a giant black plastic bag (which didn't work) and had my boots frozen solid in the morning. I had a blast!
Afterwards, I looked up everything that went wrong and started dialing in my gear, piece by piece. Best piece of advice I was given...camp close to the car so you can bail at any time easily...whether it's your backyard or a car camp ground. Make sure you can get to heat if things don't work out.
Winter camping is more fun for me then summer. It's more challenging and their usually isn't anyone on the trails. It's also a slower time for me so I get to go more often. Once you try it, you'll love it.