I've go with the "Lodge at Yosemite Falls" for lower cost, but fully heated rooms. There are motel-style rooms and you're close to the food court. Are there still cabins at the Lodge? I couldn't find any online. They were nicer than the ones in Curry Village 20 years ago.
I wouldn't do the tent cabins at Curry Village in the winter. But their "Yosemite Cabins with Bath" have heat and wooden walls.
The Lodge is a short walk from the base of Yosemite Falls. Curry Village is closer to the Happy Isles trailhead. Either have easy access to the Valley-floor trails and to the shuttle-bus stops. Parking is easier at the Lodge in the summer, either should be easy in winter.
We've done a lot of travel with a infant in a chest carrier – Black Forest in Germany, Katmai National Park to watch grizzlies, and many local, winter hikes. Bring lots of baby wipes (in an inside pocket – they stay warmer that way).
I'd suggest something like a "Pak-n-Play" as a portable crib. They you needn't worry about the baby rolling against a wall heater, etc. Although either lodging option might have cribs available.