When it's cold out my legs get really itchy. the skin isn't dry at all but it turns red.

It depends,,,: This might be just sensitivity to cold or be a contact dermatitis, like with whatever clothing you might have on your legs or it might be from the kind of soap you're using. It could remotely be from some of the meds you're taking, like the Advil (ibuprofen). It might also be from a cold agglutinin disease or antibodies that react only in cold weather. It'd be smart to see your doctor for allergy tests.