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If they charge a fee for the carts regardless of the person's condition then it is legal. The issue is whether the disabled are treated the same as others. While there are come legal requirements as to special accommodations, the provision of golf carts haven't been found to be an accommodation that is required.
There would be an issue if the golf course refused to allow any carts which would mean, inherently, that a person with a walking disability couldn't play but under the facts you describe the golf course isn't doing anything illegal by charging everyone to rent golf carts.
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Of course, please feel free to ask any follow up questions or questions to clarify issues in this thread.