When we lived in LA, my wife and I belonged to Mountaingate Country Club. We had 27 holes and the course was located in the Santa Monica Mountains north of the Getty Center.
We walked and carried our clubs (not pull carts). In fact, the club did not allow pull carts and the idea was to force members to rent electric carts. They could not ban walking and figured that few would carry their clubs up and down the hills.
JPPE, electric carts are a little wussy for a stud cyclist like you.
I understand that many courses do not allow pull carts but most allow you to carry. I prefer to walk. I like to stay focused on my game and driving around in a cart seems to cause me to lose concentration.