Cold urticaria and cold sores are totally different things. As you know, cold urticaria is caused by a reaction to cold exposure, but cold sores are caused by the herpes simplex type 1 (hsv1) virus.
Hsv1 can be triggered by lots of things, including other illnesses and cold. So while they aren't related, they might be triggered by the same things. If you continue to get outbreaks of hsv1, you might want to talk to your doctor about suppressive therapy, like taking valtrex or acyclovir daily.
I hope things improve for you soon!