Hello Lauren,
I believe that you're a bit premature in searching for your ancestor John Schroeder in Saxony as you don't offer enough info for other researchers to connect.
I say that because there is much untapped information available on John and his family here in Michigan.
So far you've located him on the 1860 census in Detroit.
Viewing that census offers the following clues:
Since all of the children born at that time were born in Michigan, the oldest having been born about 1845, tells me that John and Margareth were probably married in Detroit sometime around 1844.
You shouldn't have any trouble checking the marriages for Detroit prior to 1850 ...there wouldn't have been that many John Schroeders.
Also, because you only checked the 1860 census, you missed some of the children that were born after that date.
On the 1870 Michigan census, John Schroeder and his family had relocated to Owosso, Shiawassee, Michigan.
The family consisted of the following persons:

John Schroeder, 49, b. ca. 1820 in Saxony,
Margareth, 45, b. Hessen-Cassel
Frederick, 13, b. Mi
Charles, 10, b. Mi
William 8, b. Mi
Henry, 6, b. Mi

In 1900, John, 79 and widowed resided with his youngest son Henry and wife Emilia. It was here that John stated that he immigrated in 1844 and that he was a naturalized citizen. The 1900 census also states that John was born in Dec. 1820.

Here is what I suggest you do:
Contact the library in Saginaw to see if you can find the death dates of John and Margareth and possibly an obituary for both of them. In those days, the obituaries frequently stated where the family lived before they came to the US.

John's son, Charles Schroeder, also farmed in the nearby township of Bennington.

Then, after you have some definite birthdates and perhaps the maiden name of Margareth, you can list your query on the message board and possibly link up with another researcher in Germany.

Best of luck,
Ursula from Michigan