I have left mine in the car on a Battery Tender a couple of times, my garage is not heated. I worry about the battery location in the C5 sitting right above some critical components (electronic and vacuum lines etc.) so for the last couple of years I have taken it out and stored it with the Battery Tender on.
As BF says get out and enjoy that car, that W word is still a long way off.
Best thing to do is either purchase a battery maintainer, or just disconnect the battery. There is so much draw from the computer in the C5 that I've found the battery can no longer start the car after 3 weeks of sitting (in my case).
However, if you plan on starting the car every two weeks or so to keep the battery up, that should work too.
Store mine in an unheated garage although it is attached to the house.
Make sure car is clean and dry, Sta-bil in the gas tank (go for a short drive) .
Hook up to a Ctek charger, and I never start it until the spring.
Put steel wool in exhaust pipes to prevent lodgers.
Also put 40psi air in tires, not sure if that's really needed but it doesn't seem to hurt.
Fires up like a new car in the spring
Did this every year except for last winter when it stayed at Manny's spa.
You might also consider going to your local marina or RV dealer and getting a tub/container of "No - Damp"
These are dehumidifier (crystals)
This can be placed in your interior (floor) and absorb water in late fall and spring as the weather changes during the day and night
Check the tub regularily during these times
You'll be amazed at how much water collects in the tub. Keeping moisture out of your interior.
- usually under $20