It could be they are hut sites. There were many winter camps in your area. Most huts were built over a dug out area about one or two feet deep the size of the hut. Took less material to build it that way. Dig around in the ends of the pits and see if you run into any bricks or burnt wood.

They could also have been rifle pits for picketts or part of the trench. Top of a hill is a good spot for observation.

Latrines were not dug in the trenches unless the soldiers manning the works were under fire and could not make it to an area behind the lines for doing their business. In areas of non-combat, sick soldiers who died usually did so in some sort of hospital or house if it was available. I doubt they are grave sites.

Sometimes it is difficult to tell what happened 140+ years ago by landscape features. A lot can change in that period of time.

Hope this helps.