I guess if we were to look at the situation both in its wording and its context...
The wording being used, emphasised with the use of the word very, does imply a specific focus on the soul, and even the mention of souls in regards to freezing something either has to be referring to metaphysical soul hax, or just total and utter nonsense, not unlike saying you'll burn someone all the way down to their sense of fashion, which has to either mean the speaker has something absurdly wrong with their mind or that their fire somehow carries extra hax.
Throw in the fact that manipulating souls, and intangible objects that can still be interacted with, is so common that it's basically a default attachment to demon power, and there's a bit pointing at soul freezing here.
Returning to that admittedly stupid analogy of burning someone all the way down to their sense of fashion, the situation we have here is pretty close to the character making that above threat, which as said above has to either mean the speaker has something absurdly wrong with their mind or that their fire somehow carries extra hax. Now let's say that this statement take place in a verse where similar characters frequently remove aspects of people's minds including their way of thinking and their skills. In this analogy, we'd have a fair bit of reason to think the elemental attacks might have the extra hax, given that the exact same hax is attached to loads of things.
I know the analogy is long-winded and ridiculous, and I apologise for that. Still, the fact that the statement is either sheer nonsense or a hax claim, in a verse where that exact hax is everywhere, is worth considering.