No, you don't have to remove your water for freezing weather.

I drain a little water down to get the pump and hoses off, put them inside and forget about it until next year. It's like any container you put in the freezer without a lid: the water pushes UP not OUT. You save the cost of adding water and salt every year.

I don't bother with a cover anymore because all it does is collect all the stuff from the trees and air anyway, mixes it with the snow and it all winds up in the pool no matter what you do. I throw a black tarp over it when the snow starts to melt and it starts heating the pool: it's unbelievable how much and how fast it heats 5000 gallons of ice. Grade 5 Science stuff, Folks. Been working for me for a few years now, I highly recommend it.