Okay, from that I get the impression that Gimli didn't consider himself worthy enough to ride such a great horse.
But from the movie I got the impression that he didn't wish to ride at all. Am I misremembering?
I'd hate to think I'd have to watch it again. ;-)
In the movie he is portrayed in TTT as not being a good rider. He gets on and has a hard time getting the horse to go during the warg attack, and he falls off at another point.
It sounds to me like in the book he's got a case of sour grapes: "Who wants to ride a stupid horse, anyway?"
In this context, however, I took "great" to mean "very large in size" rather than "noble".
Plus, it may be a Gimli thing, rather than a general dwarvish thing.