Outhouse? I doubt it.
Look at the Mexico, NY structure. It has a large sliding door the full length of the structure. Outhouse have swinging entry doors about the width of a standard door.
I can't tell from the Rail City structure. Could be an outhouse.
As for the Carlton, NY structure. Again it has a large sliding door the full length of the structure which seems to disqualify it as an outhouse.
So I'm going to say that Mexico and Carlton are more likely to be some type of equipment sheds.