Can an Elemental Bloodline Sorcerer Use Rime Spell on Their Fire Spells?

Question

The elemental bloodline's bloodline arcana feature grants the sorcerer the ability to change the energy damage a spell deals from its "base" energy damage to the energy type of their bloodline (cold, for instance):

Whenever you cast a spell that deals energy damage, you can change the type of damage to match the type of your bloodline. This also changes the spell’s type to match the type of your bloodline.

The feat Rime Spell states:

The frost of your cold spell clings to the target, impeding it for a short time. A rime spell causes creatures that takes cold damage from the spell to become entangled for a number of rounds equal to the original level of the spell.

This feat only affects spells with the cold descriptor.

What does "spell type" mean in the bloodline arcana, and can I use it to change, say, Fireball to a coldball and use Rime Spell to entangle the enemies damaged?

Related questions, but not addressing the issue of the descriptor changing or not with this bloodline arcana: spells still get their effects, which spells qualify for damage change. Searching "sorcerer elemental bloodline rime spell pathfinder" on this site had no results.

Answer 1

Yes, they can.

The descriptor, in that context, is part of the spell's type.

This means that, if you cast flaming hands being a cold bloodline sorcerer, you can change the spell from Evocation (Fire) to Evocation (Cold). With the descriptor change, the spell's type has also changed.

Otherwise, there is no mention of what exactly is a spell's "type" in the core rulebook. A "spell's type" is only mentioned four times in the core: Summon Monster/Natures Ally I, the Elemental Sorcerer Bloodline, and Aiming a Spell, which mentions Spell's Type and Spell Description right after the other.

You must make choices about whom a spell is to affect or where an effect is to originate, depending on a spell’s type. The next entry in a spell description defines the spell’s target (or targets), its effect, or its area, as appropriate.

And on the summon spells:

When you use a summoning spell to summon a creature with an alignment or elemental subtype, it is a spell of that type.

There is confirmation that those terms are used interchangeably with the same meaning by an ex-developer, Sean K. Reynolds, back when he worked at paizo. The community has understood that when a text changes a spell's type, it is probably talking about the spell's descriptor, or another term that identifies the spell.

Keep in mind, however, that there are other references to type used in a different context, such as when they must separate divine from arcane (and now psychic) spells. They use the term spell type there with another meaning than what is discussed here.

Answer 2

Yes, Rime Spell should work on a spell changed to cold damage by the elemental bloodline feature

The critical part is the statement that:

This also changes the spell’s type to match the type of your bloodline.

Spells don't actually have types (or subtypes) as the wording of the Elemental Bloodline suggests, but they do have descriptors, and the only sensible way to interpret this ability is that it changes the spell's descriptors.

Since a modified spell would replace the original energy descriptor with the [cold] descriptor, any spell so modified would be eligible for Rime Spell's effect.