Trouble,
Do not leave that charger on your battery at all times unless it is the small wall-wart "maintainer" that keeps it at 12v. I've used automatic "Battery Tender" types and also "Fully Automatic" chargers on batteries over the winter and the batteries always fail after a few years.
Those "AUTOMATIC" battery chargers will still kill your battery over time by keeping the cells over charged.
For Winter storage, fully charge it then disconnect it, or use this maintainer described below.
The "maintainer" is sold at Harbor Freight, usually on sale for $4.99 and will not CHARGE a battery but will keep a fully charged battery at 12v so it doesn't fall below this level. This will keep you battery alive and not over charge it.
No matter how how much you pay for your AUTOMATIC charger, it will kill your battery if you leave it hooked up too long.