Although the 1890 census was almost totally destroyed, there was a Veteran’s Schedule done at the same time. It’s possible your Civil War ancestor will show up on this. It documented around 75,000 Civil War Union veterans or their widows.
According to the census office, this is the information collected, “name, rank, company, regiment or vessel, date of enlistment, date of discharge, and length of service. It also included the post office address, any disability incurred in the service, and general remarks.” Some of the census takers ended up recording Confederate veterans and veterans of other wars. Read more about the Veterans Census on the National Archives site.
To get something looked up in this Veteran’s Schedule, there’s a special angel out there willing to search for free. Just one search request per person, per day. Allow a week for the look up. The site is called Ancestral Findings and here is the form to submit your request.
I’ve just submitted mine for Abraham Bates Tower. Can’t wait to see if anything turns up for the searcher. Wish me luck.
UPDATE March 6, 2015: Had a reply on my inquiry on the 1890 Veterans Schedule and no luck. Sigh.