13 mph is faster than joggers, and certainly faster than I'd want to go on sidewalks -- in my neighborhood, anyway. I take the street whenever possible, but if I can't -- if it's too narrow, too busy, and too fast -- I'll find a sidewalk and take it easy.
Anyway...... back on topic...
If I wasn't already wearing glasses, I'd certainly wear something to keep the wind out of my eyes. Tinted, clear, Oakleys, Foakleys, whatever; if my vehicle doesn't have a windshield, I'll get a mini version for my eyeballs.