You don't need goggles.... but I would say that some sort of eye protection is a necessity.
On bright sunny days, there will be a lot of reflected light and a lot of glare looking back up the hill and at the end of the day when the sun is low on the horizon. You could get away with sunglasses, but if you have the kind that 'cup' your eyes then they will probably fog up quickly when you aren't moving.
On overcast days , the cold wind is usually still a factor. You might be alright standing still, but you will probably have to squint once you're sliding down a slope at 20 mph.
If you don't like goggles then maybe you should try a monocle or two. A monocole and a top hat. Don't forget the fob watch!