As this is a central point, where CCM is different to other Civ 3 mods, here is a screenshot showing the situation of the knights in the moutains (
http://forums.civfanatics.com/showpost.php?p=9241459&postcount=322) , that have lost the road on the mountain:
These knights now can only enter a mountain, that has a road on it, if they use this road, so they have to move via an accessable file that contains the road leading to the mountain.
So the knights could enter a mountain via the red route in 3 turns over two fields of plains to another field with plain, an irrigation and a road, that continous its way on the mountain, or
the knights could enter a mountain over the blue route, moving two tiles over plains to reach a road that leads on the mountain.
The knights can also move over hills, as in hills movement for knights isn´t forbidden (only slowed down).
Mountains that don´t contain a road on them that is continuing to a field that is allowed for that unit, can never be entered by the knights.
I hope, this helps a little bit.