I think there's two reasons for this. 1. We're conditioned to view left to right movement as advancing, as is typical in movies and stuff. Not sure if movies are the cause of that conditioning or an effect. 2. Maps have north on top, east on the right, west on the left, so we default to interpret it as if the viewer is facing north and Washington is moving west to Pennsylvania.

The painter lived for a time in Philadelphia so I doubt he was confused about the geography. I guess the left-right movement conditioning wasn't a thing in the 1850s, or he would have painted them facing the other way. Or maybe he wanted to depict the return trip since they crossed at night, but that'd be a weird thing to paint.