I agree, use the 3M adhesive. I want to add that it comes in two colors, the natural yellowish color and in black. I prefer the black because it doesn't contrast with the color of the weatherstripping. Both work equally as well, it's just a little neater looking in black when the excess squeezes out on the edges. Just about all auto part stores carry it.
Make sure to clean all of the mold release agent from the weatherstrip and clean the mounting surface before you apply the adhesive.
Yes, it does get cold in Savannah. I'm freezing here in Jacksonville. Old man Winter has been working overtime this year, that's for sure. Good luck.