Or you can do it poor-boy fashion and turn a wood mandrel. Turn a spindle that is say, 1" in diameter. Measure the length of your horn tip (let's say it is 3" long). Reduce a 3" section of the wood spindle to the diameter of the hole you've drilled through the horn tip (1/4" for instance), then lightly sand it to reduce the diameter just ever-so-slightly. Mark your spindle and the lathe center so you can return it to the same position, then remove it from the lathe.
Saw through the center of the 1/4" diameter, and shorten one side by 1/4" or so. Insert both ends of the spindle into your horn tip, and return it to the lathe. the horn tip will be held by compression from the ends, and the spindle will keep it centered. You may have to dink around a bit to get it turning true, but once you have it you can begin turning the horn.
You could do something similar by attaching the spindle to a wood block mounted on a faceplate. It is a little easier to set up (there's less of the feeling that you need another hand to get it all set up) but either way will work.
