There are several things that can cause damage to above ground swimming winter pool covers.
One of the first things to do is make sure you have your winter cover installed properly. Improper installation can cause severe damage to your cover. Another thing that can cause damage is to have to little or too much standing water on your cover. You will want to keep some water on top of the cover to weigh it down, however you get a large amount of water on top of the cover you will want to pump some of the water off using a cover pump.
High winds can cause heavy damage to the covers, if the cover isn't secured properly,it can cause rips or tears in the fabric. To help prevent high winds from causing too much damage you should make sure you have the proper amount of water on the cover, and in high wind areas you may also want to use a winter cover seal that wraps around the pool or cover clips.
If your pool cover gets ice on it , wait for it to melt do not try picking it off of the cover. Many times when a person tries to remove the frozen ice they will puncture the cover.
Here are some steps to follow to winterize your above ground swimming pool. http://www.royalswimmingpools.com/winter.htm#aboveground