How can I find the county from which my ancestor came?

Henry,

Have you found Michael's death record? These sometimes include parents' names and/or birthplace in Ireland.

How about his obituary/gravestone?

Sometimes probate records refer to relatives in a certain county in Ireland.

Have you looked at all the census records he appears in to see if any relatives from Ireland were in the household--or in the neighborhood?

 

I hope these ideas help.

If he was Catholic (as opposed to being a Protestant of English ancestry), then there's a decent chance that he came from County Clare.  The Irish surname Ó hÍommhair, which originated there, was frequently anglicized as Howard (and also as O'Hure), and I noticed a number of Howard's from Clare in the Family Search database [https://www.familysearch.org] .

In fact, FS has several Michael Howard's born in or around 1840 who ended up in Iowa, so you might check out the records there.  The database is free to use, once you create an account.

We have not found an obituary, but I have photos of his headstone and have visited the cemetery in Iowa where he and some of his family were buried. We don't know his religion, and have not found any probate records. So far there is nothing that identifies any family members either in Ireland or in the U.S.