First things first, and this could save a few bob, get the battery condition checked.

DO NOT TRUST DEALERS. They know sweet FA. When the battery starts to get iffy the charge drop can cause the alarm to start doing funny things. Combine that with the fact that the cold can affect the battery and you may well have reason why it's picked a hell of a time to start acting up.

Having said that, as others have said, the original alarm was a POS. Go for a good aftermarket system and it'll be far superior.