Ice-fishing is historically incredibly important. You can catch fresh protein that way pretty much all winter long... when most birds worth eating are long gone and deer are pretty hard to find, and scrawny at best. It's a lot easier than tromping around all day in the snow looking for a couple squirrels or bunnies.
It's called a shack or shanty. Some folks go completely bonkers with 'em... generators, heaters, TV's, the whole nine yards. At the peak of the season you'll see hundreds of 'em on the lakes in WI and MN.
On a related note, I used to see posters up north for "IceHole" peppermint schnapps that depicted two guys ice-fishing. The caption read,
"How come Bob doesn't come fishing with us?"
"His wife lets him drink at home."