Hey guys.
A trickle charger is designed to maintain your battery. It can slow-charge your battery up to full, and then keep it there. You can use it while it is plugged into the car, or not. Some vehicles have a large "power draw", especially if they have anti-theif systems installed (boomerage, alarm, etc). I always suggest unplugged the battery, and then using the trickle charger. The best solution is to actually keep your battery inside your house.
As for starting the car in the winter-time, we all know that cold weather starts are bad for the engine. There is no oil circulation for those first few seconds, the oil is thick, and since the car hasn't run in a while, there is no 'left over' oil still providing some lubrication like you have when you drive the car on a daily basis.
You put the same amount of wear on the engine, when you start it after 1 month, as you would if you started it after 6. The engine doesn't care. So why bother starting it every month. It doesn't help, and it doesn't "fix" or prevent anything.
Oil doesn't go bad, but it does take all the crap from the engine. Moisture, Metal particals, gas... There is a reason why there is a 'time' requirement for oil... 5,000km OR 3 months.
Do yourself a favour. Put the car on a charger, don't start the car, and just wait until the spring comes.
When it comes, there will generally be tips on what you can do to help the wear when you start the car for the first time; but if it is an OEM street car.. just turn the key!
By the way; SilverDub... In your picture, it doesn't look like the negative is connected in the right spot. It's not on the main grounding cable???