When jumping from a car, I would turn the car OFF. This is the safest way because it's the same 12.6V battery, just bigger. If the car is running its voltage regulator will try to compensate for any voltage drop. So, when you crank the bike, the car's voltage regulator adds more juice, and as you stopped cranking, a momentary spike is inevitable until the car's voltage regulator scales the voltage back. It's OK if the voltage spikes to 15-16V, however significantly more than that... who knows what might happen.
For this reason, even when jumping car to car, I would turn the car off because when the other car/bike starts, the two charging systems fight with each other. That's why every instruction says to disconnect cables immediately as soon as the other vehicle starts. While in most cases, nothing bad happens, I think there is an increased chance of something going wrong with one vehicle or another.
Also, your battery didn't go bust because of the cold. Something else is wrong, and I would suspect your tender. I am a strong advocate of avoiding tenders, and has been for many years. If the tender failed to maintain your battery and is discharged, it has mostly water and not acid. In warm season, it's not so bad - you just charge it, and no harm done. Not so when the temperatures were below freezing. Water freezes, pretty much destroying the battery in the process.
If you don't ride for a period of time, just take the battery out indoors, charge it and leave it alone for up to a few months. Charge again before the next use. Or, charge it once a week overnight, and then disconnect from charger.
