of course it can. if the antifreeze is old or isn’t strong enough then yes, bits like the waterpump would freeze, though this wouldn’t prevent the engine from turning, when it did turn, you’d get an expensive repair bill.
If you have a gasket failure, then coolant can leak to within the moving bits of the engine and could freeze there and seize things.
If there is nothing at all – ie. no sound like it’s trying to turn when starting, then a much more likely explanation is that the battery has either discharge (did you leave your lights on?), or that the battery has failed. Especially in this weather, battery’s can just completely give up the ghost. Happened to me one summer, started fine in the morning, drove an hour, parked up, shopped for an hour, battery completely dead on return.