The windshield wiper motor is protected by a circuit breaker and a fuse. If the motor overheats due to heavy snow, etc., the wiper will stop until the motor cools.
If the overload is caused by some electrical problem, have it fixed.
Headlamp Wiring
Power Windows and Other Power OptionsChevrolet Cobalt Owners Manual. Winter Driving
Driving on Snow or Ice
Drive carefully when there is snow or ice between the
tires and the road, creating less traction or grip. Wet ice
can occur at about 0°C (32°F) when freezing rain
begins to fall, resulting in even less traction. Avoid
driving on wet ice or in freezing rain until roads c ...