Here's what I recommend, if you absolutely can not plug in any installed accessories:
1. Have your battery tested. This is free at AutoZone, Napa, and Carquest. Probably other places too. Replace it if they recommend.
2. While there, get one of the cheap battery terminal brushes, a couple anti-corrosion felt pads for the terminals, and a can of anti-corrosion spray. If your battery terminals are loose, pick up some shims too. All told, you'll be up to about $20. Clean your connections, install the felt pads, the shims if necessary, and then spray the connections.
3. Don't bother with any gas additives unless your engine sounds rough or hesitates. If that happens, just add a bottle of Heet. Red bottle for fuel injected cars.
4. Consider getting a battery jump starter, for those rare occasions you leave your door ajar or something. It happens to us all sometimes, but it happens very frequently to those of us with kids.
I grew up in the middle of Canada, I now live in Fairbanks AK. If you were going to winterize for a really cold climate, there are a lot of accessories you could add (battery tender, battery heater, oil heater, tranny heater, coolant heater, etc) but they all require being plugged in. Some people install a main switch for their battery, just in case anything is left on, but that's a poor option for newer cars.