That's what I did when I was in college. Lots of people rode bikes to school, and then walked them once on campus because 1) that's what the campus rules were - no bikes/skateboards/rollerblades on the walkways, and 2) if you tried to ride a bike on the walkways you would plow into several pedestrians almost instantly, because they were typically full of college students and professors going to classes.

If your walkways are less crowded, then maybe you can get away with riding a bike on them, but don't pretend that there's a rule that says people have to travel in certain directions on certain sides of the walkway just because you're mad that you got hurt.