I roll my dough on the top of my freezer chest. Unless you live in the tropics, you can wait until it is cold outside and open the window. I bet plenty of Christmas cookies are made in a cold room.
Also, there are ways to decrease the water content of the dough without compromising the flavor. For example:
1. use rendered butter.
2. leave out eggwhites or replace with powdered eggwhites.
3. use more concentrated "flavor oils" instead of "extracts."