I got more curious about this and did some more research. I had limited time since I need to get to work soon but I did find a few things about whiskers and their function. From various sites, I found that whiskers serve a much more important function in cats, and wild canids as well. They are indeed a sensory hair, similar and compared to an antennae. I doubt in a domestic dog there would be any real noticeable difference in a dog with or without whiskers, but there IS a difference to them. I don't want to get into quoting a bunch of places and certainly I'm not arguing to cut or not to cut whiskers. My main point here is that they are a sensory organ, and I did my research out of curiosity and wanting to know accurately what their purpose is.

This is from the Singapore Science Centre (www.science.edu.sg):

Dogs also have long, stiff whiskers about the muzzle. The whiskers are also highly sensitive touch organs. A dog's whiskers may sense the wind direction and so help the dog determine the direction from which an odour is coming. These whiskers occur in clusters and serve as sensory structures - anything brushing against these whiskers stimulates the dog to close his eyes, pull away, turn his head, paw his face, or shake his head. Some exhibitors trim the whiskers of their show dogs to give the dog's head and face a smooth look. More importantly, it gives the judge a nice smooth feel in the ring. But such trimming may limit the dog's response to his environment and detracts from the natural appearance of the pet.
There was much more extensive information on how whiskers serve cats, and wild canids.

So no, trimming the whiskers on a dog wouldn't cause bumping into walls or any other dramatic difference like that. I'm guessing that their function has probably decreased in domestic dogs through the thousands of years of domestication, when a dog does not need every sense on alert in order to fill its belly.