One of the issues involving the use of aquarium type pumps is that
they are diaphragm pumps. When the diaphragm gets cold it stiffens
reducing the ability to move air or create any pressure. If you put
your airstone deep at all, as I do to get it below the ice pack, the
pressure created during cold weather may not be enough to move any
air.

The solution is to keep your pump warm with some kind of heater or use
a different type of pump.
I agree about a different type of pump (piston, outdoor type), but they are
expensive and have found the Optima acquarium pump works well at 2" - 3"
deep in my pond - I replace the diaphragm assembly every 3 yrs and have had
no trouble since (I was using a smaller, cheaper one that broke) I just keep
making sure the ice dome doesn't get thick (another story!) and make sure
the bubbler is bubbling
Gale :~)