COLD AS ICE= Extremely cold (he's not referring to temperature, but to the way he treats her). It is a very common comparison: it's (as) cold as ice. In these cliché comparisons we often drop the first AS in the comparison: it's black as pitch, it's hard as a rock, he's mad as a hatter (a reference to the Mad Hatter of Alice in Wonderland; mad = crazy) etc.

BITTER= sour, acid, acrid. But again, he's referring to his character, the way he treats her. If a person is bitter, he is resentful, sarcastic and/or full of anguish and sorrow. He compares this with December because December is a cold month with unpleasant, bitter weather (bitter weather is harsh, unpleasant, very cold, rainy, etc). But more than that, he refers to a "December winter night", which is even harsher than during the day. Of course, we are talking about the northern hemisphere December, wintertime.

TEND= If you tend to do something, you feel an inclination to do it, you often do it.

LOSE MY TEMPER= If you lose your temper, you lose control and become very angry and aggressive.

I CROSS THE LINE= I go too far in my behaviour, I do or say bad things that are too bad, more than what is tolerable.

IT GETS HARD= It is difficult.

LEAVE YOUR SIDE= Leave you.

NO MATTER WHAT I SAY= It doesn't matter what kind of things I say; even if I say that I will leave you, it's not true, I won't.

CAUSE= (coll.) Because.

WANTED= /wɒntɪd/ in BrE, but in AmE it is often pronounced /wɑnɪd/ (N+T often = N, and /ɒ/ in America sounds /ɑ/)

I WOULD HAVE GONE= This is a 2nd conditional sentence (IF+Past + Would) so it refers to a condition that is impossible or very difficult (in this case it's impossible because we use the perfect conditional, so we're talking about something that could have happened but didn't). Let's analyse it deeper:
- If I wanted to leave, I would have left by now
IF I WANTED TO LEAVE- The simple past in the if-clause is called "unreal past" (or "past subjunctive"). In modern English, its form is exactly the same as the normal past, but the unreal past is not used to talk about what happened in the past, but to talk about a present situation which is not real, for example, a supposition, a wish, a hope, etc. When he says "If I wanted to leave" he means, "I don't want to leave, but let's suppose I want", and the second part of the sentence gives the answer to this supposition: "I would have left" (but I haven't, I'm still here), so if I am still here, it is because I don't really want to leave you. Consequently, you must not believe me when I go crazy and I tell you that I hate you or treat you unkind.

BY NOW= Before this time.
We use "by" with time expressions to say that something happens, or must happen before that time, earlier:
- Please, bring me your compositions by next Tuesday = I want your compositions before Tuesday, so you can give them to me today, tomorrow, etc. or next Monday, but next Tuesday would be too late.

TO KEEP MY MIND OFF THE EDGE= The EDGE is the limit, the border of something (here, the line separating sanity from insanity/madness/craziness), and OFF expresses the idea of separation, so if you keep my mind off the edge, I don't go crazy, you help me to be sane.

ALL ALONG= Always, from the beginning.

PRETEND= To give a false appearance, to make believe something which is not true.

IT DIDN'T MATTER= It wasn't important.
This past is, again, an "unreal past" (see above), so it means that it did matter, it was important. The complete sentence is: "I tried to pretend it didn't matter if I was alone (or not)" = I pretended that I didn't care about it, I could be alone without you, no problem, but that's not true, I needed you.

DEEP DOWN= (also: deep inside) We use this phrase to express what we really feel/think inside, as opposed to a different idea we give to other people:
- She looks very nice and good, but deep down, she's bad and selfish.
- I said I didn't want to go with her, but deep inside, I wanted her to insist.

IF YOU WERE GONE= Again, another 2nd conditional with the unreal past, so it means that you are not gone, you're still here, but let's imagine (unreal) that you are not here, what would happen? I'd be lost without you. The complete sentence is: "If you were gone for even a day, I wouldn't know which way to turn" (I wouldn't know what to do, how to live).
TO BE GONE= To have left, not to be here:
- Too late, he is gone = He is not here (we can also say: "he has gone")

KIND OF= (coll.) More or less.
This phrase is so common that it often means nothing:
- I kind of feel tired today (this may mean that you feel a bit tired, or simply that you are tired, but you insert that "kind of" just to make the sentence longer or sound colloquial).
We can also use it to make something softer, not so strong:
"She's kind of stupid" is not so strong as "She's stupid".

DARK= Talking about personality, a person who is dark is somebody who is or looks evil, bad, especially in a mysterious way, like they are hiding something.

(I) LET IT GO TOO FAR= If you "let it go too far", you lose control (see "I cross the line" above)

OBNOXIOUS= Extremely unpleasant.

AT TIMES= Sometimes, now and then.

TRY AND SEE= (coll.) Try to see.

DON'T LET ME DOWN= Don't disappoint me (don't leave me, don't stop helping me)

I WOULD DIE WITHOUT= complete sentence: "you're the only thing in this world (that) I would die without" = If you are not with me, I'll die; I could lose any other thing, but if I lose you, I'll die.