Remember, this a song written for a husband and wife to sing at friend's parties that then got used in a film. The song is about two people who
want to have sex with each other. This is a fact; not a guess or opinion or interpretation. The characters both want to have sex with each other, but this was during a time when "good" girls weren't supposed to have sex, let alone
want to have sex.
Here is just her "side." It is essentially an inner monologue--her thoughts in real time--where she is trying to come up with any rationale/excuse for
staying, not leaving:
I really can't stay. I've got to go away. This evening has been so very nice. My mother will start to worry; my father will be pacing the floor, so really I'd better scurry, but maybe just a half a drink more. The neighbors might think. Say what's in this drink? I wish I knew how to break this spell. I ought to say, no, no, no sir. At least I'm gonna say that I tried. I really can't stay, but baby, it's cold outside. I simply must go. The answer is no. Your welcome has been so nice and warm. My sister will be suspicious. My brother will be there at the door. My maiden aunt's mind is vicious, but maybe just a cigarette more. I've gotta get home. Say lend me a coat. You've really been grand, but don't you see? There's bound to be talk tomorrow. At least there will be plenty implied. I really can't stay. Baby, it's cold, baby, it's cold outside.
Note that no one is plying her with alcohol. The "drink" is
not alcoholic. That's the joke. She wishes that it
did have alcohol in it so that she could use that as her excuse. Again, that's a fact, not an interpretation. We know this from the songwriter's own daughter. And it is she who first asks for more regardless (just after noting the top of the hit list; her mother and father and what they will be thinking is going on).
In regard to saying "No," she
first tells herself that she
ought to say "no" which is immediately followed with "At least I'm gonna say that I tried."
Everything in the song is tied to repressive sexual/social mores--mainly for the woman--and her internal struggle with them. I want to stay and fuck, but "my mom and dad would flip, my sister will be suspicious, my brother will be there at the door waiting for me and my maiden Aunt's mind is
vicious and what will the neighbors think"? But then in response to
that side of the argument she's having with herself, she also says fuck all of that, I'll take another half a drink; I'll stay for just one more cigarette.
And then--finally--she goes back the other way and the social mores
win.
You've been great, but everyone will talk about it tomorrow--implying something far worse than what the two of us have--so I really can't stay.
And then they
both sing:
Baby, it's cold--meaning, the sexually repressive world outside--
baby, it's cold outside. Double entendre.
Just add in his line from the very end (in parentheses):
I really can't stay (get over that old out)
Baby, it's cold
Baby, it's cold outside.
Get over that old excuse. It's cold (sexually repressed). Then they end in perfect harmony (for the first time in the entire song), saying:
Baby, it's cold outside.
It's both physically cold outside AND the sexually repressed mores of their day are outdated and old and
both agree. Which is why it's such a brilliant and clever and empowering song (ironically) for women and men of that era. It's saying that two consenting adults should be free from the "old outs"--all of the worries about family and society and "vicious minds" that will imply something sinful was going on--when in fact it's two people having a wonderful time together wanting to have sex without any judgements from society.
To perhaps a lesser extent, the male character is also playing his role in the socially enforced and thus pointless dance that they both know they are doing, but not in any "rapey" sense at all. They are
both wanting the cold old world of sexual repression (religious oppression) to leave them alone and let them be free to have sex with each other.