1. Reaching her hand to her face, her fingers touched her freezing cheeks.
Is the free modifier incorrect, as it seems to be referring to her fingers instead of her?
I agree with everything said before me. Too many "her"s, and the false concurrence of events.
These issues aside, some suggested trimming the sentence, and I think both options are valid, but have a slightly different purpose:
1. "She touched her freezing cheeks." This is short and precise. To me it seems to underline the action itself, and the fact that her cheeks are freezing cold.
2. "She lifted a hand to her face and touched her freezing cheeks." This is more drawn-out, conveying a sense of suspense, maybe even horror. This focuses more on the atmosphere of the scene, which I cannot divine from a single sentence.
2. She shut her eyes, her mind swirling with fear as she stood amidst the chaos.
Is "swirling" the right verb form here? Should the clauses be swapped? Or should "her mind swirling" be replaced with "as her mind swirled"?
I like swirling. It provides a concurrence that I enjoy, along with the "as" part at the end. Now, again, different formulations have been suggested:
1. "Amidst the chaos she shut her eyes, her mind swirling with fear." As BethS said, this provides order and causality. It also starts with chaos and ends with fear, which perhaps focuses on the horror.
2. "She shut her eyes, her mind swirling with fear as she stood amidst the chaos." (The original.) This is non-linear, but that is a valid way to tell a story. The reader isn't certain why she's shutting her eyes; why her mind's in a swirl. This adds an air of mystery. Also, it focuses more on the character herself, starting with "She shut . . ." and ending with ". . . as she stood . . ."
What I'm trying to say is: it all depends. The more critical problems have already been pointed out, but the stylistic choice remains, and has to fit the relevant context.
My two cents. And everything I said might be completely false in context; maybe the context lends itself to a different interpretation entirely.
EDIT: All examples of formulation are shamelessly stolen from BethS. Also, Harlequin suggested a different version of #2 that I sadly didn't notice. Anyway, my intention was to convey the effect on the feel of the sentence, not to give a comprehensive account of all possible options, so I'll leave it at that.