Woods attended Cathedral High School in Indianapolis before playing college basketball at the University of Kentucky. As a Wildcat in 1992, he was a member of a senior-laden team colloquially known as the "Unforgettables" who had come to Kentucky in 1988 and had stayed with the school for all four years, despite the NCAA putting the university's basketball program on probation for three years, including a ban on post-season competition in both 1990 and 1991, for recruiting and academic violations in 1989.