2001 Suburban brake freeze

For the last 3 winters in a row, my emergency brake line (?) has frozen during extended cold periods, below 30 degrees. I can feel the transmission slip into reverse, but when I give it gas, it refuses to budge. (Yes, I have released the emergency brake!)



I have had the vehicle towed to the dealership twice for this problem. Of course, it refused to perform for the technician. Once the weather and/or engine is warm, the issue goes away.



Any idea how I can solve this problem? I have resorted to backing into my driveway on cold days. As long as I don’t have to drive in reverse, it works just fine.