When the pool is closed down for the season there are still somethings you want to keep an eye on when it comes to automatic covers. Just like in the summer you want to maintain a normal operating level of water. Low water level can pull on the cover stretching it out as well as putting strain on the cover tracks and coping.
Cover pumps should always be left on and plugged in while the cover is closed. Too much water on top of the cover also stretches and pulls it. Keep an eye on the cover pump and notice if it is ever pumping water when theres limited to no water on top. Pin hole leaks can allow a cover pump to pump out the water in the pool which is also dangerous.
Keep in mind that the top couple inches of water will probably freeze at some points in the winter. If the water level in the pool is touching the cover and the water freezes, you won't be able to open the cover.