Is there a function to curving the spokes, or is it purely for aesthetics?

From my limited experience with cast iron objects, the metal tends to shrink as it cools.

Thinner portions cool and shrink faster and can 'hot tear' away from their connection point to thicker places, which tend to remain molten longer. If you cast a wheel rim, straight spokes, and hub as a single unit, the shrinking can cause the spokes to snap. If you change the spoke to a curved shape, the shrinking spoke will straighten out slightly but not be as likely to snap or warp the rim.

At least this is the reasoning that I've had explained to me.

Personally I think it's a combination of function, metalworking myths and aesthetics.

I am not sure if you have noticed in any of my photos, but basically all of our wagons have the very same style of wheel for the handbrake of each wagon. Its quite an amazing aspect, I have to agree.