No.
The feat applies to all attacks after being activated.
I would think the answer to be "yes"
You hit with cold --> Activated
Cold Damage --> +5 from vulnerability
no?
Its when you hit its activated, and you hit before you deal damage? or?
The general rule is that if an attack hits, it does the damage determined by the hit (shy of an immediate interupt disrupting the damage, but that is an exception to the normal rules, specific beats general). The DMG even indicates that a player should roll both at once.
The general rule is not if an attack hits, it adds properties to the attack and then the damage is calculated based on those new properties.
Do you have a page reference for this general rule? I don't seem to be able to find anything that explicitly states the sequence in which damage and effects of an attack that hits have to be resolved.
When you hit, you usually deal damage and sometimes produce some other effect.
Page 276. There is no sequence. Both occur simultaneously. So, assigning the Vulnerability before the Damage in order to make extra Damage occur would be giving them a sequence (and a sequence in the opposite order of this sentence).
Would you see any difference in the resolution of Hypothetical Power X (Cold) and Hypothetical Power Y (Cold) with the following hit entries?
Hit: The target gains vulnerable cold 5 until the end of your next turn, and you deal 1d6 cold damage.
and
Hit: You deal 1d6 cold damage, and the target gains vulnerable cold 5 until the end of your next turn.
Hence, simultaneous as far as we can tell.