Exercise in winter

I get exercise induced urticaria, specifically when the air temp is cool (in-/outdoor) so I find it difficult when I want to go for a walk or something during winter. I haven’t been able to find a way to prevent or mitigate the symptoms so I thought I would see if anyone has suggestions. I don’t take any medication for it so I don’t usually keep anything on hand other than Benadryl/diphenhydramine.