Characters riding monsters are not affected by fear and terror in the same way as the creature they are riding. See the Psychology section for a detailed explanation of how this works. For example, a dragon causes terror and so is unaffected by fear or terror - it is a huge monster and is hardly likely to be upset by smaller less frightening creatures. A dragon rider is also immune to fear and terror. Perched on top of a huge dragon his courage is bolstered beyond the point where he has to worry about such things.
If a monster is subject to some inhibiting psychological effect, such as hatred or stupidity, then the appropriate tests must be made. However, all leadership tests can be made using the rider's leadership characteristic. This represents the rider's ability to control the beast and impose his own will over the creature's natural instincts. If the monster is affected by frenzy, stupidity, hatred, or whatever it will carry its rider along with it, but the rider himself is not affected by the psychological reaction. So, if a monster goes stupid and is unable to fight this does not affect the rider, who may fight on as normal.
The same rule applies to monsters pulling chariots: any psychological tests are taken using the best leadership value of the chariot crew.