Will my vinyl above ground pool be damaged if I drain it but don't take it down and store it this winter?

With a Vinyl Liner you should not empty it OR take it down. It's very hard to get the liner back in place if you remove it. Vinyl shrinks as it ages so you also need the weight of the water to hold it in place. Movement of the liner could also cause older vinyl to crack. Think of an older cars dashboard!

To winterize the pool you should lower the water just below the skimmer, plug the return line, drain the skimmer, pump, filter and Plumbing and cover the pool with a winter cover.