*** Distance between greens and tee boxes
*** Overall terrain
*** Distance from clubhouse to #1 tee or #18 green back to clubhouse
*** Weather (i.e. heat and humidity)
*** Volume of play on the course in question
*** Age/fitness level of participants
*** the pace of play battle between riders and walkers (whether the actual issue is imagined or not the surface level conflict remains!)
Rock Creek
Sand Hills
Dismal Red
Kingsley
Tobacco Road
Among the reasons you've cited, heat & humidity is the number one reason I will occasionally opt to ride. I prefer to walk, but would certainly rather ride than not play. My age & fitness level work against me, but I am able to walk 36 per day for a week straight when traveling to the UK, so it's really the heat/humidity mostly. Volume of play on a course really doesn't factor in for me, but I suppose I could see it mattering for a large group traveling together.
In terms of the specific courses you mention...
Sand Hills - highly walkable, once you get to Ben's porch. Green to tee transitions are reasonable and terrain is not bad. It's a great walk, which I wouldn't hesitate to take on. I've simply followed my host's preference in every round there, which is about 50/50.
Kingsley - highly walkable. Green to tee transitions reasonable. A bit of terrain to traverse, but nothing too onerous. Clubhouse proximity not an issue. On my one visit, I played 5+ rounds, all walking, including >36 in a day.
Dismal River Red - walkable, if logistics to/from clubhouse are worked out. Terrain not too severe, transitions good. Rode most rounds during 5th Major, but found the holes I did walk pretty pleasant.
RCCC - tougher than average walk, but still doable. Some tough terrain main issue. I followed my host's lead, which was to ride, and loved every minute on property, but would have walked at least one round, otherwise. Probably a walk in the AM, ride in the PM as ideal day.
Tobacco Road - walkable, but not as pleasant a walk as others cited. Probably easier overall than RCCC, but long (and some odd) transitions in a couple of spots make it less practical or desirable.