No... he didn't make it up... I remembered this passage, and that Gimli did indeed ride with Legolas.
There was great wonder, and many dark and doubtful glances, among his men, when Éomer gave orders that the spare horses were to be lent to the strangers; but only Éothain dared to speak openly.
'It may be well enough for this lord of the race of Gondor, as he claims,' he said, 'but who has heard of a horse of the Mark being given to a Dwarf?'
'No one,' said Gimli. 'And do not trouble: no one will ever hear of it. I would sooner walk than sit on the back of any beast so great, free or begrudged.'
'But you must ride now, or you will hinder us,' said Aragorn.
'Come, you shall sit behind me, friend Gimli, said Legolas. Then all will be well, and you need neither borrow a horse nor be troubled by one.'
A great dark-grey horse was brought to Aragorn, and he mounted it. 'Hasufel is his name,' said Éomer. 'May he bear you well and to better fortune than Gárulf, his late master!'
Maybe it's just the difference between horses and ponies?
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. ;-)