What damage type is empowered when Ice Storm is cast by an evoker?

Question

The party Evoker has just reached 10th level and gained Empowered Evocation

Beginning at 10th level, you can add your Intelligence modifier to one damage roll of any wizard evocation spell you cast.

While most of his evocation spells do a single type of damage, he does have access to Ice Storm, which does

2d8 bludgeoning damage and 4d6 cold damage on a failed save, or half as much damage on a successful one.

It could matter which type of damage has been empowered, for example when the target has a different resistance, immunity, or vulnerability to bludgeoning vis a vis cold.

Which type, or types, of damage are increased when Ice Storm is cast with empowered evocation?

There are related questions already on this site addressing, when there are multiple damage types, which damage type...

the Sharpshooter feat applies to ranged damage

the Sneak Attack class feature applies to damage

damage-reducing effects like the class feature Cutting Words reduces

The consensus from the answers to these questions is that even though the damage itself counts as "one roll", it does have components of different types of damage, and that damage increases are applied to one type, only. These answers also affirm that there is no RAW for which damage type is increased, and as such mostly advocate for allowing the player using the ability to choose.

However, in the case of my question, I am leaning towards saying that the damage increase applies specifically to the cold damage, because flavor-wise cold feels more like what would be enhanced by evocation magic (the bludgeoning is more like conjuration, I think). A good answer will either support or refute my opinion on this.

_{Note this question is about whether empowered evocation applies to just one of the damage components of Ice Storm, or both. In their answer, wax eagle says "which damage type it falls under is not addressed, and as such I would allow the wizard to pick. If you want to do something consistent, always applying it to the first damage instance would make sense". This is a possible answer to my question, although I would prefer that it address my assumption that it is more natural for the ability to apply to the cold damage.}

_{Finally, for what it is worth, this is the same evoker PC as is referenced in this question.}

Answer 1

RAW, you can choose either type of damage to which to add the bonus.

You quoted the relevant rule (emphasis mine):

Beginning at 10th level, you can add your Intelligence modifier to one damage roll of any wizard evocation spell you cast.

Since there is no indication of which type of damage you should add the bonus to in the case of multiple damage types, you are allowed to choose which roll to empower.

The argument about cold damage being more related to the Evocation School is reasonable.

The Evocation School's lore tells us that indeed the damage types inflicted by the spells belonging to this school are more related to elemental-like damages rather than to physical ones, even if there are some exceptions (Arcane Hand, Earth Tremor). Anyway, as gto mentioned in the comments, another interpretation may suggest that the wizard creates more and/or larger chunks of ice, thus increasing the bludgeoning damage. In this way, the bludgeoning damage is ultimately still caused by the evoker's facility with elemental magic.

A 10th level wizard is a master of the Art: they are able to channel their power wherever they like.

A wizard that has reached the 10th level is powerful and experienced: even if their specialization is in the Evocation School, their knowledge and mastery of the Art would allow them to easily choose which type of damage increase.

Answer 2

Whichever you like

“you can add your Intelligence modifier to one damage roll”. Ice Storm has 2 damage rolls - you can so you choose.