The warhorse gains extra D8's at the levels which the chart says he does.
If you've got Defenders of the Faith, use the chart for the celestial warhorse, if you haven't, just make use of the standard paladin chart (it's only one off in this case I believe).
The war horse gains extra d8's, base attack bonus, and base saves as his hit dice go up. Since the mount becomes a magical beast when it becomes a paladin mount, your DM may rule that it gets feats and skills with it's bonus hit die as per the advancement section in the Monster Manual. Then again, he might say it doesn't specifically list them so he might not. He also might say as a celestial warhorse, it is an outsider and advances as such, up to him.
Once he gives you a type to advance in, just have a look at the big chart in the front of the Monster Manual (or the advancement section in the System Reference Document).