We've always rented a cart when we stayed at the Fort. But if someone didn't want to spend the money on it, I wouldn't tell them that they HAD to have it. I personally would make it happen for myself. If that means skipping on other extras while on the trip than I would. Having the cart is just very convenient and fun.
Make sure you call and reserve one before your stay if you want one. They don't charge you until your trip but they may all be taken if you wait to try to get one. Call 407-824-2742