Russ, when I was buying an onion, I gathered up a whole bunch of loose onion skins that where laying in the produce bin at the super market. Loosely I probably had a third of an ice cream pales worth.
When I was ready to dye the horn and rings ( I did them all before assembly) , I put about 1.5 gal of water in a pot big enough to hang the horn in and added all of the onion skins. I them heated to a boil and immediatly shut off the burner and then suspended the horn, fully submerged. I let it soak like that for 40 minutes. Then I took it out and let it cool in the house and then air dried it outside as I got the rest of the stuff ready for final assembly.
This is all just to give it a little color. You can hopefully see the difference in the photos from the beginning of the post to the last.
Most people from what I gather, use store bought RIT Dye and do the same process.