We just spent the weekend up near Hector Ferguson Lake, and we just printed three one-day tickets and put them on the dash. We looked, and there are no signs anywhere saying anything about not parking overnight. So I figured I'd just write "Do no tow. If there is a problem, call ----" and my wife's phone number.
In the end, everything was fine and my car was where I left it when we returned. They clearly don't mind people doing this, as they must know the parking machine is useless.
Also, as an aside, I should mention that the machine would accept plastic as well, not just coins. So that does make things a little more convenient if you forgot coins.