I live in canada, pools freeze solid over the 3 months of cold we get, I don't use a winter cover since it does nothing other than try and wreck my pool when the winds get a hold of it, don't have many trees close by though, but the nice thing is my pool is easy to open and allways clear since i start it up before the warmth gets to it.
Those neighbours with winter covers seem to delay their openings because of all the extra work involved, they always have the swamp going.