Aussie, you did not ask about the button... but just in case you don't already know what it is:
It is a US Army button, dating from 1902 onward. That was the year when the army first adopted the Great Seal for use on its uniform buttons. However, your button has a raised rim/border around its edge, so it is from 1910 or later. I say "or later" because the very same emblem is still being used on US Army buttons today. But assuming you found it at the same place your found the bridle-rosettes, your button is most probably from the 1910-to-1930s time period (or perhaps as late as the World War Two era). If you can read the backmark (maker's-mark) on your button, tell us what it is, because we might be able to give you a more-exact time date, based on when that specific button-supplying company was in business.
If your button has gold plating on its front, it was worn by an Officer. It is wasn't gold plated, it was for Enlisted-men's ranks (private, corporal, sargeant).