A fully charged flooded deep cycle battery will not freeze until about -80f. The amount of charge makes a large difference on what that freeze point is...Less charge and it will freeze at warmer temps. More:
http://www.trojanbattery.com/pdf/WP_...orage_0512.pdf
I have four motorcycles that have to be stored during our cold winters and only one battery tender for them. I leave the tender on the BMW all the time and only disconnect it to place it on one of the other bikes. I leave it connected to one of the other bikes for a few days once every couple months...then back on the BMW.
Typically for trolling motor batteries (true deep cells) I would plug them in once a month for a few days. I do the same with the camper. Last year I didn't even plug the camper batteries in over the entire winter but I did check them...if a battery shows a drop in charge, I will plug it in. It is very cold here and this slows the discharge rate...-My habits don't apply for everyone and are not perfect.
I'm not familiar with the charger you linked. Some chargers are 'smart' and leaving them plugged in is the best thing you can do for the battery. The charger I use for the bikes is 'smart' and has different processes depending on the state of charge.
This is a subject that could turn into a large amount of reading.
A full battery is not drawing power but the charger itself is still using a very small amount even if it is not charging. I would follow the instructions on your charger and forget about it...including the cost. After a little research a small tender like I use on the bikes is certainly less than a buck a month.