The Anchorage Museum is open. That's worth a few hours. They also have a pretty neat built-in science center that would occupy your daughter for awhile.
https://www.anchoragemuseum.org/visit/
Otherwise, get a rental car (they're cheap in the winter) and drive around a bit--if you're comfortable driving in winter conditions, that is (they do keep the roads pretty clear). There's some amazing scenery very near Anchorage (head south to Girdwood, where the big ski resort is). Or head out to Kincaid Park and watch the planes land over cross-country skiers. Or join those cross-country skiers!
The "touristy" things might be closed, but don't let anyone tell you there isn't anything to do!