Mark Fine,
Broad fairways designed and built prior to motorized transportation gave way to narrower fairways and broader roughs with the advent of irrigation systems, especially, center fairway single line systems.
This transition or transformation can provide the corridors necessary to insert cart paths, although in certain situations, there might not be an ideal or compromise solution.
But, for the most part, some creativity combined with traffic control can provide a reasonable solution.
Finding the ideal route is the biggest problem, hiding them is quite simple, provided the club wants to spend the additional money to shield them from the golfers eye. While the amount of money required isn't enormous, it's still a line item, and one that can be easily targeted by a membership trying to save money.
Sometimes tees need to be shifted without disturbing their tactical use, in order to accomodate cart path access.
Each golf course, and each hole must be intelligently analyzed, in a vacuum if possible, to avoid predisposition, or resistance to change.
Start with topos and aerials and then go on site.
Good luck.