As a tip - if you go out earlier, there are fewer people around and therefore more scope for nudity. I'm a big fan of outdoor nudity and I do it all the time. Around 3.00am seems to be the best time - tends to be too late for people coming home and too early for people getting up.
I've previously left the house naked, been out and about for about an hour and then returned without seeing a single person
As another tip - adrenaline is a great way of you not noticing just how cold it actually is