Well, I am home. Landed last night around 12:30am and the car showed that snowflake icon on the battery display (Donner Summit Mode?). When I got to the car, the display immediately said, "Very Low Battery" which I'd never seen before. It showed 26mi of range remaining and it was 21F outside. This meant a mandatory trip to the supercharger (which unfortunately is not on my way home).
I figured the 8 mi trip to the supercharger was not risky with 26mi of range, so I drove normally (i.e., turned on the heat, drove at 70mph in a 65) but after 4mi I looked down and saw that I had 12mi remaining! My 4mi drive had consumed 14mi of rated range and I still had 4mi left to go! I really didn't want to be stranded at 1am in cold weather... so I slowed down to about 50mph and turned off everything. No heat, no seat heater, not even the radio. The car began driving different... I could feel the responsiveness decline as it went into some other mode attempting to not die.
I reached the supercharger with 4mi left on the battery. Strangely, after 5min of charging, I got up to 5mi of charge. After another 5mins it was 15mi of charge. The car said "supercharging" but was charging at a rate of 27mi per hour of charge. I have used superchargers before and usually it's 200+ miles for each hour. Perhaps the cold? Perhaps the depleted state of my battery? After about half an hour, it was up to 140mi per hour, and the car had 100mi of charge so I could make it home.
Home at 2am. Exhausted.
I won't be taking my Tesla to the airport any more... it's too risky