Caring for your pond liner during winter depends on factors such as your liner material, your climate, and whether you plan to empty your pond. If you're planning on draining your pond, flexible liners such as EPDM and RPE and generally ok to leave in place, since they don't lose significant flexibility and aren't susceptible to cracking unless the temperatures dip below -40°F. If your winters include deep freezes, it's a good idea to protect the liner with a layer of mulch or leaves to minimize temperature fluctuations.
Consider your pond's depth. Small, shallow ponds may freeze solid when temperatures drop for an extended period. Since a solid block of ice can put pressure on the liner, it may be best to remove the liner in shallow ponds. Large ponds or those over 3 feet deep aren't generally at risk for this. On the other end of the spectrum, an empty pond will expose your liner to sunlight and prolonged exposure in a sunny climate can do significant damage. Consider removing or covering your liner to protect it. If you do remove your liner, thoroughly clean and dry it before folding it carefully and placing it in a dry storage space until you're ready to set it out again.