Broadfork- For me, the easiest way to count rings is to start at the tips and work back. If you will spend some time studying herds of sheep containing various age animals, you can quickly learn to visualize the type of horn conformation that rams carry at each age benchmark. This knowledge then helps a lot in being able to pick out the annual growth sections on a given older ram.
A lamb of the year, by the onset of his first winter at 6-7 months of age usually has small pointy horns maybe 3-4 inches long. Later in life most rams will have slowly busted off these "lamb tips" as they mature. Your ram has "broomed off" quite a bit of his lamb tips.
By their second winter (age 1-1/2) rams horns will look a lot like a mature ewe's horns, except wider at the base when viewed from the side, and typically about 7-9 inches long. At this age they are easy to mistake for a ewe at first glance, and often still hang around with their original family groups.
A 2-1/2 year old ram is a "sickle-horn" and is now unmistakeable for a ram even at a distance, as his bases have now fattened up considerably.
Each year thereafter the horns continue to grow outward from the base, with the annual increase in length being less and less each year, in most cases. Knowing that makes it easier to spot each successive year's growth section.