My best guess is that it's a precancel. Aside from precancels,
you weren't supposed to overprint stamps then and (I assume) now. Postal stationery indicia are assumed to be the same deal. Dealer A.C. Roessler got in big trouble for his homemade zeppelin overprints:http://goscf.com/t/63111
This is the New Haven Railroad logo of the time. Queries sent to a couple of New Haven collectors turned up nothing like this. The couple (earlier) postcards I was shown had plain indicia. The railroad's historical society site only shows a few documents. Is anyone here a member that might be able to dig further?
Is there something printed on the back that might give a tiny clue as to what it might have been used for? Also, does anyone have a similar postcard from a different railroad? I've never seen any other, though that doesn't count for much since there are all kinds of postal card usages around.