Shadow Conjuration

[DanMcS]

"Shadow conjuration can mimic any sorcerer or wizard conjuration (summoning) or conjuration (creation) spell of 3rd level or lower."

"Shadow objects or substances have normal effects except against those who disbelieve them. Against disbelievers, they are 20% likely to work."

Phantom Steed isn't a summoning, it's a creation. The steed still probably has 1/5 hit points, and can be disbelieved, but it should still have its normal movement rate (20'/caster level) unless you disbelieve it, right? If you disbelive it and are its rider, does it travel at 4'/caster level?

 

[Jack Simth]

You just need to look a little further down in the description....

A shadow creature has one-fifth the hit points of a normal creature of its kind (regardless of whether it’s recognized as shadowy). It deals normal damage and has all normal abilities and weaknesses. Against a creature that recognizes it as a shadow creature, however, the shadow creature’s damage is one-fifth (20%) normal, and all special abilities that do not deal lethal damage are only 20% likely to work. (Roll for each use and each affected character separately.) Furthermore, the shadow creature’s AC bonuses are one-fifth as large.

(emphasis added). If the person trying to ride the steed believes it, everything works just fine (barring damage to the steed, of course). Someone who disbelieves the steed has a 20% chance of being able to ride it anyway, but once riding it, has few difficulties.