Does Lasting Frost affect the damage dealt by a Frost Weapon?

Question

Lasting Frost

Benefit: Once per turn, the first target you hit with a power that has the cold keyword gains vulnerable 5 cold after the attack. The vulnerability lasts until the end of your next turn.

Frost Weapon

Power (At-Will • Cold): Free Action. All damage dealt by this weapon is cold damage. Another free action returns the damage to normal.

Lasting Frost is commonly used with Frost Weapons in the DPR builds over at the wizards CharOp forums. Example here.

However, I'm not convinced that it works due to the emphasized language in the lasting frost quotation above.

Does attacking with a Frost Weapon convey the cold keyword to the weapon powers you use with it?

Answer 1

From the Rules Compendium (pg 115):

If a power gains or loses damage types, the power gains the keywords for any damage types that are added, and it loses the keywords for any damage types that are removed.

Also, Cold is listed as a Damage Type on page 114.

Answer 2

Yes.

Effectively the Frost Weapon's power having the cold keyword is what allows this to work. It is an always on effect on the weapon. Thus it provides the cold keyword to any power that uses the weapon's damage.