Are poisons that you apply to weapons instanteneous?

Let's say that I have a Bow with is enchanted with Frost. Now I take a Weakness to Frost/Ice x% potion and poison the bow.

I shoot at an unsuspecting Skeever and hit it.

Does the potion-weakness go into effect fast enough that the poor Skeever get the extra damage from the weakness of the arrow that just hit it.

Same question of course for Fire and Lightning.

Solution 1:

It sound too good for me. As I found on usep.net

Weakness to Poison has to be applied prior to a dose of poison for the weakness to take effect. For example, if the enemy is not weakened and you use a poison with Weakness to Poison and damage, the damage will not be affected by the weakness that time but the enemy will be affected in later uses of the poison.