Several men of the House family served in Arkansas. Many appear with initials only, and there are a few with the initial “M,” either as a first name or a second name. The only Matthew that I found is Mathew (one T) W. House, Company H, 6th Arkansas Cavalry (Monroe’s).

If this is your man, a synopsis of his service record is available at:

http://www.couchgenweb.com/civilwar/6cavcoh.html

If this is not your man, perhaps more information can help separate him from all of those “M” initials. For example, do you know his middle name, or where he was living in 1860? Even the smallest clue can be helpful.