FRONTERA SPORT alarm goes off when Frosty?

Hi there, I own a 1999 frontera sport which is great. The only problem is that in the winter when its cold my alarm goes off (seems to be only when there is frost on the car)! ( Normally between 12 and 4 AM) I think its caused by frost covering the windows or maybe a drop in temperature which is affecting the battery and then the alarm?? Does anyone know the answer? I took to main dealer last year. They replaced the backup dead battery pack alarm under the wheel arch and now it just goes off with twice the noise!! AAARRRRGGGGHHH!!!!. Have resorted to leaving it unlocked when frost is predicted, but dont always get it right. ( thinking of becoming a weather man as almost fully qualified!). Any suggestions on a remedy would be greatly appreciated. A tired Wayne...