Its 2 degrees where i live, went out with damp hair and had dinner not too long ago. will i get sick because i went out with wet hair in the cold?

Probably not: Getting cold does not cause one to get sick. This time of year most illnesses are caused by cold and flu viruses. Getting cold might lower your resistance a bit but you will not get sick unless you have been recently exposed to a virus and if you were exposed you will likely get sick whether you got cold or not. See https://www.healthline.com/health/does-cold-weather-make-you-sick#implications