Typically not. Book and lab fees do vary, however.

That’s rare in the US. Generally a credit hour has a fixed cost + incidentals like textbooks or occasionally lab fees.

I remember a 1 credit hour horseback riding class having a rather steep extra fee attached to it.

No...I've heard of this happening in Australia. Its a very sad state of things, but even if they wanted to do something like that, it would be impossible, since American universities are organized usually into just two or three colleges (School of Arts & Sciences being the largest, comprising of everything from CS to English to Physics to Psychology; then there's usually an Arts school--music, painting, etc.--and/or an Engineering school and/or an Agro/environmental sciences school), and you share courses with everyone in your college, and the majority of your classes are not actually for your major, so most students end up learning a great breadth of things and engaging in pet interests (I myself was always interested in historical linguistics). If you charged less for a CS degree, you'd just get a lot of shitty CS students who are only in the major because they want to do something else. And oftentimes engineering/arts degrees are more expensive anyway, since they are seen as purely professional training.

It's true, unfortunately. If we had more funding for public universities, the aid would be re-appropriated, but for now they're struggling to make it affordable for students who are just "average."