My search-fu didn't turn up any specific threads on this topic, so here goes ...
Frostbite (UM, level 1) and Frigid Touch (UM, level 2) both are low-level spells with touch attacks which do cold damage (non-lethal in Frostbite's case) and have a rider effects (Fatigued from Frostbite, Staggered from Frigid Touch). There is no saving throw at all, though Spell Resistance does apply in both cases.
When dealing with regular damage, the rule has always been that if Damage Reduction negates the damage, then the rider effect is likewise negated. (For example, injury poisons riding on a bite attack.)
Does the same rule apply to energy resistance and rider effects?
(In my opinion, it seems cheesy to the extreme that a cold immune creature is still Fatigued or Staggered by these spells. Even the Rime Spell meta-magic feat from UM specifies that the cold damage must "go through" before the Entangled effect can affect the target.)
Anxious cold resistant and cold immune monsters/NPCs await any useful replies! :)
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For frostbite, the fatigued condition goes away when the damage does. If there's no damage, then there's no fatigued condition. For frigid touch, it seems that the staggered condition stays even if the creatures are cold immune, but as DM, you could easily rule that the staggered condition is a rider.
To be honest, spending a 2nd level spell only to stagger a creature for a round is incredibly minor use of a standard action, so I wouldn't worry about it.