I must say this thread really opened my eyes to the world of private clubs. I've been looking into a local membership and I thought I had asked every question in the book while making my decision. Based on this thread, I went back and asked if pull / push carts were allowed for walkers (previously thinking this was a no-brainer.) I got back "No, they are not allowed."
Some on this site will think I'm crazy based on a simple issue like this, but I'm seriously re-thinking my decision at this point. This particular club doesn't have a caddie program (I'm almost 100% certain anyway.) The caddie program is the one semi-valid argument I could see for not allowing the push carts.
I'm definitely more closely aligned with Mr. Huntley's comments and thinking on this issue.
I'm fully capable of toting my bag around and I probably would do so for a good portion of the year. At the same time, during the hot humid summers or 30 years from now when I may still wish to walk but may not be in the same shape to carry, this could really be a bothersome policy. I realize that is their business and they have a good healthy membership number to back it up. I'm not questioning their right to have such a policy, but it certainly is disappointing in my opinion.
As I said, this thread has really been a learning experience for me.