A couple years ago I was gearing up for a big trip to Peck. I spent a couple hours making chains for my 4X4 wheeler, two sets out of old pick up tire chains. Got to peck on bare ice and found they did little for traction even with 2 big guys on it. The chains have not been back on since.
For the last 3 days had my 4 wheeler on snow covered ice (no chains), it did well except where the drifts high centered me. Chains wouldn"t have helped, in fact one other guy with chains had more trouble with the tires digging through the packed snow and getting stuck so many times that it ended his trip for the day.
I would never tell you to not have chains because the conditions that you encounter may require some but I have not been there yet. I usaully have them with me just incase.
2 wheel drive 4 wheelers would be fine on ice without too much snow but in the wind crusted and packed snow that I was in would have been of very little use.