Pumps to put on swimming pool covers

Hmmmm. Let me see...

Water pump used in "0" degrees, water freezes at... while the water in the pool may help to keep the water on the cover liquid, what happens inside the discharge hose?

This supposes "0" degrees means 0⁰C. Would be even worse if 0⁰F.

What is a "swimming pool cover pump", and does it pump water or swimming pool covers, or air?

If it's air, that doesn't freeze till it get's really really cold. Just for grins, I'll guess that your pump won't freeze till you get below -200°F. Maybe one of the big brains knows for sure.

If possible, put inner tubes or something to raise the pool cover so it doesn't catch rain. If you have to pump, I would look into an eductor. You can use the pool pump or a submersible to feed the ecuctor. They will work right down to a small puddle and are easy to move around. Like posted, you must drain any hoses before water freezes in them.