Yeah I would personally skip the peroxide aswell... You know people bleach hair with that stuff?!
So long as it's kept clean you should have nothing to worry about, the air and the antibiotic cream should do the trick, especially if it's only a small cut.
If it's seriously muddy and your worried about mud getting into the wound, then you could wrap it, but personally I would just load on the cream and you should be right, I always like to leave the air to get to the wound.
Vetodine is good (Iodine). I use that stuff for EVERYTHING!!
R.I.P ~ Bubbles - 25yo tb mare - 13.04.2011 ~ 8:30am ~ passed away naturally and peacefully in my arms