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 Service & Repair Manual. Windshield Washer Fluid Pump, Replace
1.
Drain washer solvent from windshield
washer fluid reservoir into suitable clean container.
2.
Remove front fender liner as outlined
in "Front Fender Liner."
3.
Disconnect windshield washer ...