Huron County marriage records from 1815 to present are held by:
Huron County Courthouse Probate Court 2 E. Main St. Norwalk, Ohio 44857
However marriage records from the time frame you are looking for are probably not complete -- but its worth a shot.
While I don't live in Huron County, my local library has some historical information about the county. While at the library, I checked a couple of sources for the surnames you are seeking. This is what I found during a quick search of the indexes for:
History of the Firelands comprising Huron and Erie Counties published in 1879
The Firelands Pioneer published by The Firelands Historical Society
I found no mention of David Ray or the Printz surname in either source. There was one reference to the surname Hayhurst in The History of the Firelands. This mentioned a W. Hayhurst, who was a former principal of the North Failfield Schools.
Theodore Boughton and his wife were mentioned in both publications. In the History of the Firelands, Theodore was mentioned as holding several offices in the Methodist Church in Fairfield -- he was not a minister however.
The Firelands Pioneer of Dec. 1, 1909 contains an obituary Theodore Boughton as follows: "Boughton, Theodore, was born in Grove N.Y., February 1, 1822. He was the son of John and Susan Boughton. He came to Huron County, with his parents, in April 1836. The most of his life in Ohio was spent in Fairfield Township. He was married to Hester Ann P. Claughton in May 1847. He died August 19, 1907. His children are Mrs. Emma J. Cherry, of Oberlin, Edward W. and Edwin H. Boughton, of North Fairfield."
The Firelands Pioneer of Dec. 25, 1918 contains an obituary for Anna P. Boughton as follows: " Boughton, Anna P. (Claughton), was born in Allegany, Va., October 7, 1829, married Theodore Boughton May 1,1848, and with him came at once to Fairfield, Huron county, Ohio, where she lived for over 67 years until her death Dec. 8, 1915, at the age of 86 years, She early united with the Methodist Church and was ever a faithful and useful member. Her husband died August 18, 1907."
The obit would tend to indicate that Theodore and Anna were married in Virginia, but why would Theodore, who was apparently living in Fairfield, go to Virginia to be married? I ran copies of the obits from the Firelands Pioneer. If you would like to have them, as a documented source, I will be glad to mail them to you if you will send me an address. Hope some of this is useful -- Richard