No, tried it once and I didnt like it, much prefer to hear what is going on.
Walking is a multi sensory activity for me so I like to hear everything that is going on, unless I'm in danger of hypothermia I will keep hoods, hats and gloves to a minimum - i like to feel the weather, I also like to have bit of stone in my hand as I'm walking along - dunno why but it just feels like another connection. I think much of this came from reading stuff by Syd Scroggie , the Dundee man who lost his sight in Italy in the war but continued to go to the hills and said he enjoyed it so much more even without his sight.
Having said all that I do have involuntary soundtracks in my head as i walk , usually filmscores and 90% of the time it is Lord of the Rings or Last of the Mohicans.