I would like to
buy a back-up 12 volt AC to DC converter to power the winch if the
battery fails. Please advise on how to rate the converter based on the
battery requirement.

The battery doesn't tell you the motor requirements. All you know is that
it exceeds them.

DC power supplies are expensive. Upwards of $1 per watt, and you need many
hundreds of watts.

Why bother at all? Just borrow a battery from another vehicle if yours
fails. Even a spare battery would be far cheaper than a DC power supply.