The cooler comes on with 220V to mitigate the additional heat that is generated by charging faster. Charging slower means there's time for the heat to naturally dissipate into the environment, so a cooler isn't needed. I highly doubt 220V will prolong battery life -- it will be equal, at best.110 volt and 220 volt are going to use just about the same electricity to charge the car (a quick google search shows that 220 is about 5% more efficient, that could add up over the years!).
If one is going to be in the same house for a while, it's worthwhile to install a 220 volt outlet for the 5% or so energy savings. I read (I think) in the manual that the battery cooler only activates when the car is being charged via a 220volt outlet, so you'll be able to prolong the life of the battery if you keep charging it on a 220volt outlet as well (then again, this cooler will use a little extra energy, but it's good to prolong that battery life!)