If the water is below the skimmer and sucks air - how much damage might be done to the pool equipment or is the drain at the bottom enough to protect the pool & equipment.
NEVER run the pump when it's sucking air. The pump needs water for "lubrication" and cooling. If you work the pump dry you will destroy it! The bottom drain will protect the pool plumbing but will not help the skimmer line. You'd be better off thawing your garden hose or getting a new one, rather than risk splitting the skimmer or suction line.
Being so cold will I do any damage by sparkin' up the 'ol heater? (other than to my wallet of course).
You could run the heater. Atlanta is typically warm enough that the pool doesn't freeze. This atypical weather is only going to last a couple of days so you could run the heater for peace of mind. Make sure the heater and piping is not frozen and watch the pressure when you turn the pump on.
And which is more important - trying to keep water in the skimmers, or getting the ice to melt?
A thin sheet of ice on the surface of the pool is no problem. The freeze starts at the top. You really must prevent the skimmer box and pipes from freezing and filling the pool will allow you to run the circulation pump better.