Why aren't winter bicycles camping events common as the motorcycles one?
I haven't been in an organization that would have considered arranging such event and then decided not to, so this is pure speculation. I have a guess with two reasons: weight and competing activities.

First, winter camping requires much more equipment than summer: heavy sleeping bags, warm clothing, fuel, and taken to extreme a tent with stove. These are not fun to carry on a bike, especially when dealing with snow at the same time. Powered motorcycle lets you put all the effort to maintaining balance and helps with cutting through snow.

Second, if you are camping and traveling under your own power in snow, skis or snow shoes combined with toboggan for carrying your stuff are a better choice. Instead difficult adapting to snow, they have evolved just for snow and allow you go literally off the beaten path. A bicycle would be just trouble.

Third, not directly related to winter, there aren't many cycling events like motorcycle rallies in summer either. Mass events for cycling (or skiing for that matter) tend to be more or less race-like. With motor vehicles these would be very illegal.