Proof of Snell's Law can also done by using Fermat's principle of least time on plane surfaces. Can we prove the same result for any curved surfaces ?
Yes, I do believe so. Whatever "point" your ray of light strikes on the curved surface just assume a tangent along that point on the surface. Then do the same thing that is done for the plane surfaces and you can repeat it for all the points on the surface (interface between the two optical media).