You nut. I do it all the time on mine. Traction is for pussies and yes-men.
I bet its not as muddy over there, as it is over here...
Depends on the season. My local wetlands are utterly soupy right now.
As spring is here, you could just ditch the mudguards and mount up some 32mm cx tires on your existing kit.
Old 80 touring bikes, converted to single speed and mounted with knobbies are super cheap and fun to toss around in the peanut butter of this season.