Should Ice Arrow require reagents?

To be clear, this isn't about the more general conversation about whether or not reagents should be required for all spells. My question carries the assumption that the current system is going to be implemented. So instead of analyzing whether regents are required, I looked at each spell in the air, earth, fire, and water trees and considered whether the spell is in the right tier. I also thought about Death, Sun, and the other trees but not in as much detail as they aren't fleshed out enough yet. From that analysis there is one spell that stands out as being in the wrong tier, ice arrow.

To me ice arrow is more like fire arrow or obsidian arrow. It carries the same mental picture as those spells. It carries about the same damage and like the other two has an effect accompanying the damge component. But it doesn't carry the same mental model as lighting, fireball, ice shield, or earthquake. But it is a tier 3 spell. The other arrow spells are tier 2 spells. Lightning and that group are tier 3 spells. But ice arrow is placed in tier 3. It just seems out of place. It isn't powerful enough to require reagents; the other arrow spells don't. It just seems to have been stuck in tier 3 because of the depth not breadth rule. In the fire and earth trees, the tier 1 spell is a close melee attack. Each of those trees has an arrow spell and a second spell in their tier 2 trees. But water has douse at level one and only one close melee spell in tier 2. There is precedence in the other trees to have ice arrow as a level 2 spell. It just makes sense that is where it belongs.