Hi HC -
I’ve been doing that too many times in Grasshopper, it seems. There is no “project curve to mesh” in standard Grasshopper. In Rhino, as Pascal said, you can simply project the curve onto the mesh.
You’ll find that either the 2D curve or the 3D mesh is not “accurate”. Most likely both. There is no easy way around that. There are many plug-ins that will ease the construction of roads on terrain meshes. You can probably find scripts on this forum or could take a look at a complete package such as Lands.
-wim