Biking in the winter should be no different than walking in the winter and it's still the most convenient way to get around. Here's a photo essay showing how easy and fun riding in the snow can be.
Let's say I told you that you were going to take a child between the ages of 2 and 6ish on a trip with you, and you wanted to bike around once you got there. Nothing long distance, just tooling around the city, seeing the sights, going to museums, etc. How would you do it? What options spring to mind? Would you try to check a full-sized bike and a rear kid seat for it? Or, like most people, would you start googling bike rental options in the new city?