Could I ruin my health if I move from the South to the Northeast?

I have lived in Florida since I was 7 (30 years). I want to move to the northeast but I am concerned that because my body is not used to the brutal winter weather up there I could be compromising my health. I'm afraid the winter cold will be such a shock to my body it could make me dangerously ill. I know they say weather doesn't cause sickness but I have also heard the cold lowers immunity. Anyway, I am trying to find out if there is any medical reason for me to be concerned.