Do you have to have mud flaps on a tractor if you are hooked to a trailer?

That law tends to vary by state. In North Carolina, you're not actually required to have mud flaps. Other states may require it. I've never seen anything in the FMCSR pertaining to mud flaps, and it's unlikely that the feds mandate it, considering that states have leeway in determining whether or not they want to make them mandatory.