Damages that may occur if the reservoir for the antifreeze?

Nothing will happen, other than it will just drain out of the overflow tube onto the ground.

Ok. If your coolant reservoir is filled with ANTI-FREEZE, then how would it freeze? Thats why it is called antifreeze. Typically safe at -20 degrees or greater depending on your mix percentage. SO, unless your live DEEP in the arctic circle then like I had stated before you should have no issues. On a side note liquids like many materials expand when heated and contract when cooled. The exception is when water freezes due to the intermolecular bonds in the water molecules, and since ice is less dense than water, it floats. Now these models are known to really have rust issues, which can lead to electrolysis in the cooling system that then leads to it eating your heater core. The rust can also clog the passages at the coolant recovery tank.