Our initial idea was to let the kids paint 3 boxes white.
Then we would attach them together and glue on eyes, nose, buttons, etc. As we were painting the boxes and listening to the children, we decided not to attach them together. We cut out eyes, nose mouth out of felt and foam. We attached Velcro to the back of the pieces and to the boxes themselves. This allowed the children to stack the boxes as they wished and put the features on as they wished.
I should add that we cut a mailing tube in half and made holes in the medium size box to make the arms. We put gloves, mittens and scarves in the basket to dress the snowman. The hat was actually one a child had brought from home. We even put Velcro on the back side of the snow man so two children could put facial features on at the same time. As I was cutting out eyes, noses, mouths,etc the children were picking up scraps and using them for additional features like ears, mustaches and even whiskers.
As our week progressed we decided it would be a good idea to add more boxes of varying sizes. That way the children could experiment with stacking them and make more snowmen. I don't know if we will get to that yet this winter or if it will have to wait until another time.