This looks like a fairly easy project. I might soak the skull in a strong bleach solution for a couple of days just to get it cleaned up - rinse - let dry out for a couple of days. I would tape off the base of the horns and "flock" the skull with antique white spray paint. Hold the can back several feet and just give it a light dusting of the off-white paint. You don't really paint it.

Then lightly dab some walnut stain on the antlers with a small artist's brush. You want to do this fairly conservatively - don't get the antlers too dark. A slightly blotchy effect looks the best.