If it were me, I'd powerwash the whole thing - cleaning the dirt out of all the crevices... Then, I'd run some sandpaper over it, tape off the antlers and spraypaint it.

Once you get a couple coats of flat white on there, pull the tape off the antlers andwipe them with some dark wood stain to bring out the color.

This one is painted with $2 flat white paint from walmart.