I'd replace the battery. I *do* have the keyless ignition option, but mine acted really weird when the battery was dying (never got a message about a low battery, though). Batteries don't like the cold, so if it's going dead anyway, that might explain why it's finicky.
As an aside, I would highly recommend taking the remote to your dealer and having them change the battery for you. Even though the battery will be more expensive from them, if they break it, hopefully they'll replace it for you. Mine cracked when I tried to pry it open according to the instructions manual. Fortunately, the car was still under warranty at the time and the dealer replaced it for free.
As an aside, I would highly recommend taking the remote to your dealer and having them change the battery for you. Even though the battery will be more expensive from them, if they break it, hopefully they'll replace it for you. Mine cracked when I tried to pry it open according to the instructions manual. Fortunately, the car was still under warranty at the time and the dealer replaced it for free.