Icy but fire? Might have to do with the Mark of Arhat, but I hadn't seen it before.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You swing an icy hara at a bawdy swain. A bawdy swain badly fails to block with a Dwarven hammer.
The hara lands a hard (6/23) hit that burns a sizzling wound as the stomach takes full force of the blow.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You swing an icy hara at a bawdy swain. A bawdy swain badly fails to parry with a hand axe.
The hara lands a hard (6/23) hit that temporarily knocks away the swain's breath with a scorching blow to the chest, lightly stunning it.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You swing an icy maul at a bawdy swain. A bawdy swain badly fails to parry with a cudgel.
The maul lands a strong (7/23) hit that painfully singes the right arm.
[You're winded, nimbly balanced with no advantage.]
[Roundtime 5 sec.]

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You lob an icy javelin at a bawdy swain. A bawdy swain fails to evade.
The javelin lands a heavy (8/23) strike that scalds the chest with a blow to the ribcage, lightly stunning it.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You lob an icy spear at a bawdy swain. A bawdy swain attempts to dodge.
The spear lands a solid (5/23) hit that enkindles the swain's lower back.
The icy spear falls to the ground!

(side note: Tested without MoA up, no more fire messaging. It seems this happens when the bonus damage exceeds the weapon damage, in the case of smaller weapons with low skill vs. higher magic skill)

Grammar stuff

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You swing an icy maul at a bawdy swain. A bawdy swain fails to evade.
The maul lands a very heavy (9/23) hit that chills skin and muscle as the stomach takes (the) full force of the blow.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You swing an icy maul at a bawdy swain. A bawdy swain badly fails to block with a cutlass.
The maul lands a very heavy (9/23) hit that deeply chilling the entire left bicep.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You slice an icy bardiche at a bawdy swain. A bawdy swain badly fails to block with a cutlass.
The bardiche lands a heavy (8/23) strike that glances (off) the swain's gut and numbs it, lightly stunning it.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You slice an icy bardiche at a bawdy swain. A bawdy swain fails to dodge.
The bardiche lands an extremely heavy (10/23) hit that glances the icey icy bardiche off the back of the swain's right hand.

The branded lines of fire on a bawdy swain flare a brilliant blue-white!
< You lob an icy javelin at a bawdy swain. A bawdy swain attempts to dodge.
The javelin lands a powerful (11/23) strike that chills the neck (to) a pale white with a coat of frost.

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"Game balance is sobbing over in the corner as it considers the ramifications of AoE Blufmor Garaen. Your spell slots send their condolences." - GM Raesh

The reason you're seeing fire damage is because you have Mark of Arhat on the target.

>>If you summon a weapon, 90% of the time it ignores the elemental damage component and goes to the next highest damage for messaging. (clarify: 90% of the time the instance of summoned weapon doesn't work properly)

>>So you end up with quarterstaves that do jabbing damage, etc.

When you appraise the weapon, pay attention to which damage type the elemental damage has an affinity for.

icy quarterstaff trains the stave skill.

You are certain that it could do:
somewhat fair puncture damage
dismal slice damage
no impact damage
no fire damage
very heavy cold damage with affinity for impact attacks

If you're jabbing, you might get cold damage to show up rarely, but if you use an attack that uses impact (bash, chop, slice possibly), you'll see the cold damage more often.

I thought you meant that you were trying to jab and it wasn't doing icy damage. I'll test it out and see what it does.