I have some information and a suggestion for you regarding your coatee.
According to the book "American Military Button Makers and Dealers; Their Backmarks and Dates", the backmarks on the buttons date the coat to the 1845 - 1850 period: "Horstmann Sons & Drucker, NYC, 40 Malden Lane. Listed along with W.H. Horstmann as military goods dealers in directories from 1845 - 1849. When the elder Horstmann died in 1850, the firm was dissolved." (quote from P. 52 of the cited source)
I suggest you email the information and picture of the coatee to Chris Trimble <email@example.com> Chris is knowledgeable in uniforms from the colonial period to the present. He may be able to help you identify the coatee. If the email address is not current, you can write him at P.O. Box 386, Saluda, VA 23149.
To Join the Company of Military Historians click here