I had this same problem happen on my 70’s Ford truck a few years ago, similar kind of parking brake system, you press on a pedal with your foot to set the parking brake. Wasn’t caused by freezing in my case, just a little corrosion of the mechanism inside the cab. I fixed it up straight away with some wd-40 and later after I’d used it a few more times, I put a little light oil on the mechanism. Has worked fine since. You might ask the dealer if they’d suggest some WD 40 be applied as it will help displace any water in the mechanism that could later freeze it up again.