Polymorph other "cannot change a subject into a construct, elemental,
outsider, or undead unless it is already that type," so you won't be turning a human rogue into a barghest with that particular spell. But let's assume that you have a tiefling rogue handy instead- in that case, per the spell,
The subject retains its own type (for example, “humanoid”),
extraordinary abilities, spells, and spell-like abilities, but
not its supernatural abilities...
...meaning your new barghest mount will be gaining hit dice as an outsider, but if you were to turn a human rogue into, say, a worg instead, it would gain hit dice as a humanoid.
As to the bonus hit dice granted by the Windrider, the class description is fairly specific.
Bonus Hit Dice: These are extra eight-sided (d8) Hit Dice,
each of which provides a Constitution modifier, as normal.
Remember that extra Hit Dice also improve the mount’s
base attack and base save bonuses.
You aren't advancing a creature when you make it your mount; you are granting it a temporary (if indefinite) bonus. Just as polymorphing a creature into a new form doesn't grant it new skills or feats, bonus hit dice don't grant anything more than what is already offered- hit points, base attack increase, and base save bonuses. Windriders do grant feats, but not skill points, with other class features.
How does your polymorphed mount's base attack and saves increase? By creature type. The new barghest would gain a bonus to its attacks and saves as though it had (for a top level Windrider) 8 more hit dice than normal. The new worg would gain a bonus as though it were a humanoid, not by class, meaning one good save and attack progression as a cleric. If it wants any more feats than the Windrider teaches him, or any more skill points, your mount is going to have to gain levels- by character class, as polymorph other doesn't grant any of the new form's feats or powers, unless they're movement-based... and even then the obviously magical movements are off-limits. And of course, if the mount advances to the point where its CR is higher than the Windrider's level - 3, it won't qualify as a mount anymore, so you'll need to be careful with even that much.