I've got the same camera from Wallyworld. I've used it quite a bit the last 3 weeks or so, and it hasn't "killed" any batteries yet, but the batteries do lose power in the cold, but get it back when you warm them up. It's been pretty cold too... lows have dropped down to the single digits. I keep a fresh set of 8 batteries in a zip-lock bag, in an inside pocket of my hunting jacket to keep them warm. Whenever I check my camera, I put in the warm ones, and put the cold ones in the pocket. I've been rotating the same 16 batteries for about 3 weeks, and they're still going strong.
The bitter cold does effect the film advance drive of the camera... it runs slow, but it still works. If you'll be checking it every morning & evening, here's a little tip to keep it working in the cold. Get some of those disposable toe warmers. Put one in your boot and walk around a bit to "smash" it flatter than it is when you take from the packaging. Then remove it from your boot, and take it out to your camera, and stick it inside.
Your camera (and batteries) will stay nice and warm for about 8 hours. The warmer won't fit right out of the package, but walking on it some flattens it just enough that it fits inside.
P.S. On my other thread about trail cams, that picture I attached of the buck was taken at 1:25 am on Thanksgiving morning. The temperature at that time was about 10F. The camera had been in the woods for about 10 days straight by then... but it still worked perfectly, thanks to the toe warmers I put in it every afternoon at the close of hunting hours.