Based on the preventative maintenance standards for heavy duty trucks, here are the minimum tread requirements:
Steer Tires: Require a minimum of 4/32" (3.2 mm) of tread depth in every major groove. They are critical for steering control and blowouts on steer axles are highly dangerous.
Drive and Trailer Tires: Require a minimum of 2/32" (1.6 mm) of tread depth.
Source Material
Preventative Maintenance Module (Topic 12) - Section 4: Tire Inspection