I wouldnt think the head gasket would go from freezing
It does sound like something froze from what you have described, if your block did freeze it would disslodge the core plugs or crack the block both are very serious but its possible another part of the coolant system froze causing poor flow and then the overheating problem.
Driving the car whilst overheating to the point where it conks out could be very damaging and could blow the headgasket/warp the head.
If it is a freezing proplem the noise from your dash would have been the heater matrix either filling or leaking due to moving ice.
I check the antifreeze to attemp to access its strenght if it just looks like water then it probably did freeze, but even if it looks good i would replace it with new stuff anyway to be safe.
Other than that i would try to get the car indoors, a friends garage or a work shop and when you know the whole system is defrosted, then run it and look for coolant leaks core plugs would be a huge leak but anything could have bust, water pump, radiator, heater pipes, thermostat housing etc.
It however posible that the problem is completely unrelated to the cold and just a coincidence. In which case it needs more looking at.