When we introduced our kids (4 & 6 years old) to winter camping, we started out for one night on a nice early spring day, and set up camp about the distance of a 10 minute ski from the snopark parking lot. The good weather made it possible to have an enjoyable time, and look forward to future trips. Being close to the parking lot made it easy to bail if things went sour. My wife was the backpacking and winter camping adviser for the area Boy Scouts. If possible, she would set up a similar scenario for the scouts for their weekend winter camping trips. I think she and our daughter may have gone on more Boy Scout winter camp trips than some of the scouts. Having a few good experiences under your belt really helps when encountering the "not so good" experiences.
I'll sum up my thoughts with the idea that anyone planning on any form of winter camping is wise to ask for advice, but their entry into winter camping should never be an actual multi-day trip.