I gather the assumption is that caddies are available?
That rather puts it into the upper echelon of courses right there.
For me, if a caddie is available, I like to take one at least once. It's fun. But cost factors into it as well. If a good yardage guide is available for $5 and the caddie costs $75 (normal at places like this), the extra $70 has to be well-considered.
I guess it all depends on the place, the traditions, what others are doing, etc. I surely have no hard and fast rules o this. And it's an issue for a tiny percentage of the golf I play.
Now make it walk v. ride and that's a more relevant question....
I tend to walk first, but if the course is hilly or has long hikes from green to tee, I'll ride. I have nothing to prove. I do hate carts on path though...
TH