Little Match Girl

[Leanne]

Brandon, in my opinion and experience, the repetition of a villanelle is most effective when it's matched with lines of equal (or close to equal) length and, if you are so inclined, meter. Contemporary villanelles tend to deviate a little from either isosyllabic or metric requirements but if you're not careful, the impact of the refrain can be lessened or lost.

1st Edit:
Villanelle: Little Match Girl

“I’m cold, hug me…” this is the line that gives me the most trouble on reading. I understand that you may feel that short=impact, but I disagree here. My suggestion would be a compromise between brevity and rhythm: "I'm so very cold. Hug me" (with or without an ellipsis to end)
Voice so soft it’s almost muted.
Please, someone, hear her plea… quick fix for rhythm would be "please won't someone hear her plea?"

Playing in the snow so free, inverted syntax makes this line stilted. Perhaps "in the snow they play, so free"
Except the girl who alone pleaded. I'm not super happy about these near rhymes for the b lines, but will leave them alone
“I’m cold, hug me…”

When snowstorms brew, towards home they flee, just "to" instead of "towards" will fit better
Yet no warmth is found, in matches lighted. maybe "yet no warmth blooms from matches lighted"
Please, someone, hear her plea…

Lost memories on relishes of glee; I confess, I don't really know what you want this line to say
Her breath, her wishes, languidly bated,
“I’m cold, hug me…”

Show some compassion, treat her gently,remove "some", it's unnecessary and makes the line too long
A cracked glass Camellia, yearning to be connected. This line is far too long, but I have no quick fix, it will depend on which words/ideas you feel are most important
Please, someone, hear her plea…

Why feign apathy, the licit felony, is it really feigning?
When a pastel life so despairingly pleaded?you have already used pleaded. My suggestion for these two lines would be something like:

By your felonious apathy
She is left to die unheeded

“I’m cold, hug me…”
Please, someone, hear her plea…

Just some thoughts... I am a bit of a fan of the villanelle

*oops, sorry, just realised we're in mild critique... oh well...