I have ridden Cottonwood pass a couple times this year (in fact last weekend) and snow was pretty good. I suggest taking the family up the road to Hancock and back, is nice easy ride with some small play areas. Also, the road off to the left going up leads to an old mining area complete with buildings that in my opinion are worth seeing.
I would caution against tin cup pass as it can have some nasty drifts if not groomed.