Don't use oil-based clays. Those never harden. Model magic is a popular air-dry clay that tends to be fairly lightweight. The water based clays used for pottery harden, but aren't very strong until you fire them properly in a kiln. Sculpey & Fimo are polymer clays that harden in a standard oven. Think carefully before using them, as they tend to be a little heavier.
Other options include Paper-mache, paperclay (basically ground up paper mache) or carving the horns from one of a number of different kinds of foam. The trick to getting paper mache to not look crummy is to do lots of sanding after the surface is completely dry. This sanding generally requires patience. The trick to foam looking real is to coat the surface with a layer of white-glue and a bit of water so that it fills up all the tiny little holes. This also adds a little strength.
As far as paint, in almost all cases, acrylic paints are just fine. Spraypaints are also OK on anything but styrofoam. For an extra strong paintjob, use a primer paint as the first coat over the surface.