Air mail. These were the days before good roads crossed the country, and where even an automotive trip was an Adventure which would take weeks. Horseback, you're going slow enough that you'd be able to see much smaller signs, and would be on a pretty well-trod path.
Shortly thereafter, though, a few things happened that made the arrows pretty obsolete. Mapping of course, was a big one; you could now navigate a lot more reliably through unknown territory. More importantly, a network of radio beacons was set up. Charts had lists of radio beacons, with their frequencies. Pilots could tune in to hear them repeatedly chirp their identification in morse code, and use radio direction finders to set their heading accordingly.
There's one other feature that was developed in that time period which also made pilots' navigation job a lot easier. The federal highway system meant that there were good, very visible, roads, serving as routing beacons in their own way. Pilots would, and still do for a lot of general aviation planes, route close to highways, because they're also a very obvious landmark that carves a path through the country.
