I hope I am not wrong on that one but if you say:
Let's go for a horse-and-buggy ride"
horse-and-buggy functions as an adjective and it describes the kind of ride you want to take.
If you reverse that and say:
We went for a ride in a horse and buggy, then horse and buggy becomes the means of transport as one word. You do not sit in a horse but you sit in the buggy (carriage).
It sounds fine to me, Bill.
Let's hope some bigger brains get together and explain it better.