When I was little, I would cut my dogs whiskers off (i wanted them to look like show dogs) and I got yelled at quite a few times because of it. My mom said they're there for a reason, but never gave a reason.
It could help them "feel" around, maybe when they're grazing or something.
They are used to help them see how close things are to them. One of the reasons it's so critical to leave them on, on a blind horse or a horse with cataracts. Removing them really affects the natural way they have to get around and know how close their surroundings are.