Tires are worn out once you reach a remaining tread depth level of 5/32 inches. Once you go below this level your tires will lose key safety properties such as grip, braking distance and ability to prevent aquaplaning. You will thus need to replace your car tires for safe driving.
To know once you reach it you can look at the tires if you have Driving Safety Indicators in the tread that will show the tread depth. If not, then you can insert a coin or a match tip to measure the depth. For winter tires it is more critical than it is for all-season tires, but if you change both at 5/32 you should be safe.