The fact that your car automatically shut off after you ran through a snow pile suggests that there might be an issue with the car's electrical system or sensors, rather than a problem with the fuel valve. Snow and moisture can sometimes interfere with electrical components and sensors, causing them to malfunction.
If you have already replaced the sensors and checked the fuel lines, you may want to have the car's electrical system thoroughly inspected by a qualified mechanic to identify and fix the underlying cause of the problem.