In 1868, three years after the end of the Civil War, Union Veterans declared a day for Memorial of those who fought. It wasn't until after WWI that Memorial Day began the recognition of all soldiers who fought.
There's an online book in Google books The National Memorial Day Which dates to 1870.
You can find other addresses given on Memorial Day during different years. Perhaps your characters are sitting in the audience during one of these addresses. Or perhaps they are crowd control, or could they be there because of a threat to one of the speakers?
Anyway, just a few thoughts, tidbits about how you might use this National Holiday correctly in your historical setting. Enjoy!
And if you're a veteran reading this post, thanks for your service. It means a lot to me.