Rifle

Pretty sure it was a Mosin-Nagant. I doubt the creators of this film knew much about firearms or hunting, so I couldn't say for sure if it was a deliberate choice or if they simply used what was there at the house, or perhaps borrowed from a neighbor. Cinematically, I think it worked out well. A relatively clunky, and hokey-looking weapon helps emphasize how dire their situation is, vs. a sleek and efficient looking Remington 700.

...and Mrs. Taylor sure seems to use a lotta ice, whenever he's away