A winter cover has NOTHING to do with the pool freezing, it does not magically keep your pool warm, all it does is keep leaves etc out, your pool would still freeze the same as without a cover.
Winterizing the pool is what needs to be done, living in ontario, I winterize - which means drop the water level below your return and skimmer and drain all equipment and lines. However, because i do not have trees nearby and we get terribly strong winds all winter, I do NOT cover my pool with a winter cover - it would do more damage than good in my case. Cleaning what did get into the pool over the winter is easy.

Or in some cases, winterizing consists of:

Put a plug in the return, a cover over the skimmer and antifreeze in all lines (I would still drain equipment though instead of antifreezing it.).