on my 360F1 (2002) I had the same experience when I took the car out after 2 weeks non-driving. In the first minute, the engine was not running normally and it was diffucult to get out of the garage..i've got the stop-and-go's you've described. But already after 50m it was over. It was not that cold...7-8°C.
But it's very possible that all the power, electronics etc. has to heat up but I did not had to wait 10min.
BTW...what the hell do you take your car out on that kind of weather ? I hope it was NOT snowing...I know it has that special traction control but I hope I will never use it..Driving 400hp on ice or snow...brrrr.a nightmare