The AmiableSlut was correct! Both the intake and the outtake pipes were completely snowed over. They are only six inches high, which does not seem particularly bright in a place that regularly gets big snow.
The handyman cleaned them all off and things seem to be moving along now. But they are going to have to fix the pipes so that it doesn’t happen every time it snows. Ridiculous.
The cats and I did fine all bundled in the bed with all the blankets! Thank you for the support and thoughts and suggestions! You all are fantastic.