The legal tire tread depth across the country remains the same for every manufacturer. When the tire reaches 1/16th of an inch of rubber and the perpendicular treadware bar appears across the tire, you have no choice but to change the tire. There is very little treat to assist in maneuvering, whether the road is dry, wet or snowy. It does not matter whether you are driving a super sportscar or a family sedan when that treadware bar shows. The pros at your tire care center are obliged to swap your tire out. If they sell decent retreads, you can try to keep your costs down with one.
For more info, see 5 Point Car Safety Checklist