The ornamental design for a riding helmet harness, as shown and described.
FIG. 1 is a perspective view of a riding helmet harness showing the new design;
FIG. 2 is a right side elevation view thereof;
FIG. 3 is a left side elevation view thereof;
FIG. 4 is a front elevation view thereof; and,
FIG. 5 is a rear elevation view thereof.
The broken line showing the riding helmet and buckles is for the purpose of illustrating environmental structure and forms no part of the claimed design.