In small bowl, combine thyme, oregano, cumin, paprika, onion powder, ½ teaspoon salt and ½ teaspoon pepper.
Pat chicken dry with paper towels; rub mixture evenly over chicken.
Place chicken in resealable plastic bag. Refrigerate 4 hours.
Remove chicken and discard bag. Grill chicken 5 to 6 minutes per side or until meat thermometer inserted into thickest part of thigh registers 165 degrees.
Make white barbecue sauce: Combine mayo, vinegar, remaining 1 ½ teaspoons pepper, the mustard, remaining ¼ teaspoon salt and the horseradish; refrigerate until ready to serve. Serve sauce with chicken.