Ever since this bitter cold weather hit us in Ohio (currently 13 degrees F) my antenna rotor has not been able to budge. I pressed the sync button and it still didn't do anything. I last used it on Wed the 30th with no problems, but today haven't been able to get it to do anything.

This a channel master rotor.

Any help would be appreciated.

1st guess ice is preventing movement, hope for some warming.

Does it hurt to spray WD-40 or something equivalent on it?

You can try it. Worse that will happen is it doesn't work. This is one reason I use multiple antennas, after experiencing what you are now going thru, 3 winters ago. Now I don't have to wait for the antenna to move to get reception. Just change the channel and wham bam thankyou maam'. ;)