Can I chill cookie dough overnight?

It shouldn't be a problem. Just be sure to bring the dough up to room temperature (I'd use a probe thermometer) before you start to work with it. I would do that even if it were chilled for only the 2 hour period you mentioned.

Thank you!

Yes actually it's good to chill it overnight because it gives the dough time to fully absorb the wet ingredients..

What kind of dough is this?

If sugar cookie, chocolate chip, molasses, etc. Absolutely! And I would argue this is highly desirable. I like to give most of my doughs a nice long sit before baking. Usually at least eight hours.
I find very thin cookie batter, like for pizzelle cookies, some vegan cookies should be used right away.