An no, the headgaskets on these engines rarely ever go bad, even if overheated. Usually it's the elbow(s) that will leak first, followed by the rad. A lot of times the rad. will leak when hot and under pressure then stop when it cools down. My 00 GT did this for about 4 months before I finally tracked it down to a bad drivers side tank seal that was right under the rad. hose.
Hopefully you get through the bitter cold w/o whatever is leaking completely failing. Another thought would be to pick a warm~ish day and with a cold engine degrease the crap out of it and hose it clean. This would be a good place to start so you know you're not smelling something from a long time ago.
