Of course, just like you are going to buy a nice warm coat for yourself so you can stay warm and cozy, you will get one for the little one as well. Right? Maybe some little protective booties also, although they can be a challenge for a four-legger to get used to.
At only five pounds, if you notice shivering or any other clues to your little one feeling cold, it will be no problem to just pick up the pup and put her inside your coat next to your own warm body. Voila-in two or three minutes you'll have a warm, happy doggie again!
I wouldn't leave a five pound dog outside by herself ANYWHERE in any climate. Would you?