I believe this is a two-point perspective, where there are two vanishing points that intersect. The red lines are the points of the top of the wagon, yellow are the bottom corners of the wagon.
That's about right. The vanishing points do appear to be on the horizon (as you said before your edit

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if the road and cart are horizontal. It's not necessarily strictly the case, but not by much, unless you deliberately make the road very rough.
The vanishing points get further apart as the angle of view gets narrow ('telephoto view'), and get closer as the angle of view widens. Looks about ok on Dusty's edit, too.
I think the road is too wide to be nice, and the cart is too wide and low to be realistic. You might check some ref.