Also, the battery is continually being drained and strained in the cold. The security system is a continual draw on the battery. In cold weather, the battery has less power to turn the motor over for a start, and also will recharge slower. I'd estimate a full recharge could take up to an hour of driving in cold weather. In warmer weather, this will shorten. Therefore, a few cold starts in a row and no good run, the battery will go flat requiring a jump start. Note, this is not to be confused with a dead battery that is not recharging under normal use and needs replacing.
So, in short. Best let it sit, the battery will probably go flat eventually. But running it and ticking over will only hasten this. If security is not an issue, you could disconnect the battery to prevent it going flat. But please consult the manual and make your own call on the security.