Why would a gas water heater discharge water in the winter?
Actually, this requires a system analysis to determine if it's a problem of the water heater, or a problem of your system needing a expansion tank.

For instance, if your water supply is provided with a check valve or a pressure reducing valve/regulator on its input, a water heater full of cold water will cause expansion, and without an expansion tank or an open connection to a supply (which a check or regualtor is not) to relieve pressure, pressure in the system will rise as the cold water is heated and expands.

You may be seeing this more in the winter as your water supply may be colder, so it has more potential to expand.

The valve is a temperature and pressure relief valve, so EITHER overheating OR overpressure will cause it to vent. I'm going to guess that it's more likely a pressure issue, and would probably be easily resolved by adding a small expansion tank; but I can't be sure about that without more details about your water system, or actual measurements of the temperature and pressure when it's venting.