The final section you should read when trying to determine if you have the proper standard is Conditions for Use. Sometimes this is called Significance and Use, or Use. It clarifies the context of the standard even further.

Section 5 of ASTM F1572-08(2015) Standard Test Methods for Tire Performance Testing on Snow and Ice Surfaces is Significance and Use. It states the context of the standard:

**Significance & Use of ASTM F1572-08(2015)**
Significance & Use
5.1 These test methods describe techniques for assessing the performance characteristics of tires in a winter environment on snow and ice surfaces in a standardized manner. When only snow is referred to hereafter, it should be understood that ice is implied as appropriate. 5.2 A series of maneuvers are conducted to characterize several aspects of the tire performance in snow, since a single maneuver is not sufficient to characterize all aspects of a tire's performance.

This clarifies the context of the standard as “a winter environment on snow and ice surfaces.” This is fitting for your original purpose for finding the standard, which was to design a better winter tire. ASTM F1572-08(2015) will help test your product.