Trembling in the freezing, but gentle air, Stacey looked up to the night sky, watching as her stale breaths evaporated in the nearest street light. She sat on her butt as what little warmth seemed to just flow into the concrete, not making a difference. But she only sat there, waiting for the physical pain to dull. The numb wind didn't waste time.
"She sat on her butt as what little warmth seemed to just flow into the concrete, not making a difference." This line needs "left in her" or "she had left" after "warmth" for clarity, I think. "The numb wind" in the last sentence should probably be "the numbing
wind" because, though personifying the wind as numb to Stacey's predicament works by making Stacey seem even more lonely, she's a character and the wind isn't. It's best to focus on her, I think.
Lifting a needle with a blood stained tip to her exposed arm, Stacey dipped the end into the gooseflesh, hardly feeling a thing. Clenching her teeth as vivid memories came back to her, Stacey pushed the needle in farther as she slowly slid it across her skin. Slowly, she thought to herself, biting her lip as tears started to form again. Let the pain last. At least it wasn't as bad as the mental pain. It was still so difficult to not just slash the whole arm from elbow to wrist. Maybe with some more cuts.
This paragraph is good. It actually made my stomach twist a bit.
But Stacey worked with the needle like a painter holding a delicate brush to what extent she could, shivering constantly with the breeze. At least the blood was warm when it came out. It used to be so great. When no one would except me; no one wanted to see me. But for one person. He was the one who stopped me for once. The only one who cared. The one who saw me for who I was. Not what I did. So warm to be next to; one whom I could actually embrace. Laugh. Tell funny, even embarrassing stories to. Someone I could believe. A person I wasn't scared of.
I may be a hypocrite for saying this, as I shift into first-person in a character's thoughts nearly all the time, but in this case, the first-person doesn't actually serve any purpose that third-person doesn't--besides, it'd work much better with a "she thought" in there somewhere to indicate that it's an intentional shift rather than a mistake.
As for the story itself, I think a short example of the embarrassing or funny stories would work better than saying "Tell funny, even embarrassing stories to." In short stories, telling rather than showing is all right, but if you can show without lengthening it too much, that's probably better.
Stacey dug harder with the needle, making jagged cuts as she continued to shiver; all the good memories coming in sharper than the needle. She could still remember those nights when she would stay at his place with the television on. It was usually cold at his place, but they would only need each other to keep warm. His warm arm that he would wrap around her.
Improper semicolon use in the first sentence. The second clause couldn't stand on its own unless you replaced "coming" with "came." Story-wise, the coldness of the implied boyfriend's house works well with the whole tone of things, and works as a nice bit of foreshadowing, however slight.
The cuts stung more as tears fell into them, the salt burning through. Stacey could feel her shoulder get colder; just the thought of leaning against him. The comfort of someone strong and there for you. Now it was just the wind, drifting in with the cold, passing right through her thin clothes.
Sheesh, that mental image is making me shiver. The semicolon is borderline. I'd suggest just replacing it with "with."
Gasping with the tears still falling almost frozen from her eyes, Stacey dropped the needle. It wasn't enough anymore. She couldn't live like this any longer. Not anymore. Blinded with tears, Stacey groped for the gun laying just beside her. Before placing it between her teeth, Stacey took a final look at her cut up arm, wiping her eyes with her sleeve. A word was barely noticeable in the bloody mess, and even though half blinded by her tears, Stacey could still make out that one word. "Raped."
And the sinister conclusion. Naturally, I start to look for loopholes whenever a character dies, but you've covered this one pretty well, if only because of the story's length. I would suggest a subtle reference or two to Stacey's family or lack of (a good) family, at least to show that she really has nothing to go back to.
Overall, the unity of this is good. The title contributes to the reader's understanding of the story and sets the tone at once. Everything contributes to the story and the conclusion in the final paragraph, and the "cold" theme comes across well.
However, when I got to the last paragraph and Stacey presumably shot herself, I felt kind of apathetic toward her as a character. I understood the story and the theme, but I didn't feel sad. I once told someone that believability was enough to make a likable character, but I was wrong. Relatability needs to be there as well. Unfortunately, with the length of this story, you couldn't elaborate on Stacey's hobbies, likes, dislikes, etc. I'm pretty sure anyone who's been betrayed in a relationship would be a lot more partial to Stacey, so I don't think this is a valid critique of your writing--rather, of my lack of experience.
The only other negative critiques I have are nit-picky grammar things, so don't worry about those too much. I'm sure more experienced critics could do better.