To the naysayers: get a clue.
Soooo many people have had derailers cables, derailers, freewheels etc. gunk and freeze up. BMX freewheels actually coast forwards sometimes.
Fixed just works. You have few drivetrain parts, and the ones you have are bombproof. Whatever happens, the chain will stay on, you will have drive, you will have braking even if the brake pads are blocks of ice and the rim is covered by a film of ice. You can control the braking on the rear wheel very finely, which is nice on slippery roads. A front brake is very warmly recommended, though.
Plus the slush does less damage, and a full drivetrain change is cheaper anyway.