Cookies end up Rubbery
Powdered sugar is not an acceptable substitute to standard white (granulated) sugar.  

During the creaming step, the hard sandy texture of granulated sugar creates small starter bubbles in the cookie dough.  These bubbles will expand during baking, and are integral to the finished cookie's texture.

Ideally, use the correct kind of sugar called for by the recipe.  Or, search for a recipe which specifically calls for powdered / confectioner's sugar instead of granulated sugar.