I make and keep a supply of Alice Medrich's butter cookies all the time. Love slicing off and baking one to have with my tea. I was in a hurry one day and used my freezer to quick chill it. It was very cold, but the cookie tasted different. It was more floury and less buttery. I think that is the issue of hydration that QueenSashy spoke of. I actually have found that the cookies are even better a couple of days later. That's my experience, but I'm sure it depends on the recipe.

We make gingerbread boys every year and if I'm in a hurry I freeze for at least and hour, I find no disernable difference.

Def not in the freezer. Could you make it a day in advance and refrig it for longer than 6 hrs? I don't think that would hurt it.

I think that it depends on the recipe you are using... But I could think of a couple of reasons why refrigeration might be preferred to freezing. By doing a longer rest you are allowing gluten strands to relax, to get better texture of the cookies. It also helps the flavors to combine. Finally, it allows the flour components to hydrate and the moisture levels become more consistent throughout the dough and the dough becomes dryer (which is a good thing because it improves texture).