You can snow blow frozen snow, but you can’t do it with any type of snowblower. Electric snowblowers are generally good at removing layers of ice up to 4 inches in thickness.
For anything above that, you will need something more powerful, which is at least a 2-stage gas blower. These units have augers that can crush the snow beneath them and are much more efficient when dealing with icy driveways/freezing winter temperatures.