Can cookie dough be refrozen?
It is recommended that you only freeze any item once. After you have defrosted the item it should be used up. I personally wouldn't freeze it again. You can make the cookies up and freeze the cookie after they are baked. This one would be fine.
After food has been frozen and thawed, it has a tenancy to deteriorate rapidly, so it would leave the texture and quality sorely lacking the next time you would want to use it. Your best option would be to bake the whole batch of thawed dough and then if it certainly is too many for immediate use, then to freeze the already baked cookies. This works well.
One thing I like to do rather than try to freeze a big lump of cookie dough is to actually scoop out dough balls like I would normally and after I have all that I wanted baked, I put a single layer of dough balls (not touching) on a cookie sheet and place in the freezer. After the dough balls are completely frozen, then I transfer them to a gallon size zip-lock freezer bag. That way I can take out as many as I want to bake and the rest can stay frozen until I'm ready to use them. When using this method, just remove the desired amount, place on a baking sheet and bake normally.
You can, but the flavor and texture may deteriorate if you do it multiple times.
I think I'd just bake the cookies and freeze them. But according to those Fundraiser style Cookie Dough ~ it says they could be thawed & refrozen anytime without a problem. It's listed as a FAQ.