Spiders and cave spiders don't get effected by poison.
Steps to reproduce:
1) Summon a normal/cave spider (no matter how)
2) Try applying to him the poison effect potion, /effect, lingering potion.
3) The spider's health doesn't low, if used with a lingering potion, he won't "sink" it.
The spider is seeming like not having the option of being poisoned at all, or completely ignoring the effect.
Update: in 1.9.1 Pre-3 they do "sink" the lingering potion, makes it even worse.