Not sure what the Winter ball does. Generally, the experts here recommend refraining from putting chemicals into your pool if you don't know what they do. I just closed my pool this past Sunday and all I did was SLAM the water a couple days prior and got my pH in range. It was at the high end of normal (7.8), but I have a mesh safety cover and any precipitation will bring down the pH marginally. The next time I will think about my pool is probably early November to drain a few inches from under the cover, making room for the melted snow and ice. Once the water freezes, there is nothing much else to do until Spring.
I expect my water to be a little green when I open it, but (given how my BQ conversion went) I also expect a case or two of liquid chlorine over a few day period, a brush, and vacuum will do the trick come Late April/Early May. There are some who advise adding a gallon of chlorine under the cover and circulate the water with a pump and garden hose sometime in late March/Early April. I figure I'll cross that bridge when I get to it.
Hope this helps.