I'm not sure why I typed "limited" at the end of (1), I meant to type "moderate" or something. It definitely wasn't a cold battery, it's possible it was due to the heat from supercharging, but that seems unlikely at such a cool ambient temperature. You didn't indicate whether it felt like you couldn't go faster (up to 250), the energy draw isn't up to the dashed line in the picture taken. It will be interesting to see what you learn when you try again without supercharging (I wouldn't wait until it's warmer, seeing the limit on the draw side is pretty rare [especially when the charge side doesn't have a dashed line], and you're not facing extreme temperatures, so warmer could make it "worse" regardless of whether or not there is any issue).
ETA: The "max battery power" setting the P models have (had?) would heat the battery in order to provide maximum possible acceleration, so I guess it could be that the battery needs to be warmer, but that still seems unlikely, because the supercharging and the draw should both have warmed it up pretty significantly from a temperature that wasn't that cold to begin with. Did the dashed lines and colored numbers go back to normal when you slowed down? That could be more informative as to what is happening and might be consistent to support my second guess.