For this cold spell it's a little too late, but the solution for this to add some heat-coil/heat-wire on the bottom of the heat-pump housing that you can activate in those conditions.

The issue is that the defrost mode will defrost all the ice from the fins, but it freezes again before it can all drain through the small drain hole on the bottom of the housing. It's somewhat a known issue with air source heat pumps, sadly. I've not run into this issue myself, but on a Dutch speaking forum (tweakers) there is a long thread about this modification to "survive" the cold spells with this small modification.

You can manually attack the ice with a heating gun or hair dryer to remove it, but that's a faffy.

I think manufacturers should, and probably will, add something like this themselves in the future.