The premises of this question is a bit on the far side, as I don't live in a country where the water-main doesn't drop out very often, and even though the temperature in the winter often drops into the freezing temperature the water is still not that cold.
However I would advise against using plastic bags for this purpose as suggested in another answer, unless they are recycled (which kind of goes against the general principle of the other answer).
My take on a solution assuming the water being cut off for shorter periods of time, would be to wipe clean the bowl with a paper towel, or possible use disposable plates during the repair period. If multiple persons in your household, you could have one plate each.
Depending on what you eat, and how dirty the plates get, you could wipe clean the plates quite a few times before it is unhealthy to eat from. If they get to dirty, then replace with a new clean plate every so often. This should help you get by until the water-main is fixed.