If you’re using a single counterpoise wire, I read that it should lay beneath and in the same line as the EFHW. But for an omnidirectional antenna like a vertical, it’s better to split the wire into 4 shorter lengths spread out like a cross from the the antenna base.
If you really mean a counterpoise (and not a radial) then laying the wire on the ground, heather, etc is fine (and a lot more convenient than raising it). Its part of the ground plane is to act as the ‘top plate’ of a capacitor, the ground being the ‘bottom plate’.
P.S. I never bother with CPs with my EFHWs [I always get good results without one]. If one is going to that trouble, IMO you might as well deploy an inverted-V [linked] dipole.