Civic EG

I've been starting my hatch once or twice a week and the PC680 has held a charge fine, but it's getting real cold (and snowy) out.

The pc680 is a dry cell battery and I've been told once you let it die completely, the battery (and your $130) is history.

If I started the car one more time and let it charge the battery for like 10 mins, then took the battery out and took it inside until spring, would it die?

You wont kill it if you let it die out completely. That's a great battery and will stand up to abuse. But you're right that it's a very bad to let a battery fully discharge (except deep cycle).

This is what you need. http://www.summitracing.com/parts/DTN-021-0128/

Besides using it for storage, you should install the cord permanently and hook it up overnight once a month or so.