Freezing cookies works great everyone should do it. :) Personally I use paper vellum, but that's due to overstocks from long ago. Parchement works just as well and costs less.

I pack and store my homemade cookies in coffee cans in the freezer and I always use wax paper squares (about 6 inches square) that I buy for almost nothing at our local Cash 'n Carry store (they serve restaurants and other grocery stores with products). Some cookies will dry out a bit during freezing...I always taste them to check to see how well they did. If I think they taste a bit dry, I'll melt some chocolate (white, dark, peanutbutter, etc.) and dip one side of the cookie in the melted chocolate then sprinkle chopped nuts or chopped candy, ice cream sprinkles, etc. over the chocolate.......GUARANTEE, nobody has ever complained that the cookies are dry. The cookies I do this most often are sugar cookies and Spritz . They need decorating anyway so it's OK.