For one day, the kindergarten bit might be a challenge.
There are plenty of ski resorts around Luzern you can try - Melchsee Frutt, Engelberg, Klewenalp. A bit of a longer trip will take you to the Berner Oberland. Andermatt is just under 2 hours away.
Or you might try Germany - Feldberg, for example. I've no idea about kindergarten style facilities - try the various websites.
I know people with younger kids have found
Belchen to be quite handy. But no child care - one of you has to stay with the sprog. I've seen plenty of babies/toddlers playing in the snow, sledging, being looked after by one parent.