From Dean Martin's recording:
Verse 1: Marilyn Maxwell & Dean Martin]
I really can't stay (But, baby, it's cold outside)
I've got to away (But, baby, it's cold outside)
This evening has been (Been hoping that you'd drop in)
So very nice (I'll hold your hands, they're just like ice)
My mother will start worry (Beautiful, what's your hurry?)
My father will be pacing the floor (Listen to the fireplace roar)
So really I'd better scurry (Beautiful, please don't hurry)
But maybe just a half a drink more (Put some records on while I pour)
The neighbors might think (Baby, it's bad out there)
Say what's in this drink (No cab's to be had out there)
I wish I knew how (Your eyes are like starlight now)
To break this spell (I'll take your hat, your hair looks swell)
I ought to say "No, no, no, sir" (Mind if I move in closer?)
At least I'm gonna say that I tried (What's the sense in hurtin' my pride?)
[Chorus: Marilyn Maxwell, Dean Martin & Both]
I really can't stay
(Oh, baby, don't hold out)
Baby, it's cold outside
[Verse 2: Marilyn Maxwell & Dean Martin]
I simply must go (But, baby, it's cold outside)
The answer is no (But, baby, it's cold outside)
Your welcome has been (How lucky that you dropped in)
So nice and warm (Look out the window at the storm)
My sister will be suspicious (Gosh your lips look delicious)
My brother will be there at the door (Waves upon the tropical shore)
My maiden aunt's mind is vicious (Gosh your lips are delicious)
But maybe just a cigarette more (Never such a blizzard before)
I've gotta get home (But, baby, you'd freeze out there)
Say, lend me a coat (It's up to your knees out there)
You've really been grand (I thrill when you touch my hand)
But don't you see? (How can you do this thing to me?)
There's bound to be talk tomorrow (Think of my lifelong sorrow)
At least there will be plenty implied (If you got pneumonia and died)
[Chorus: Marilyn Maxwell, Dean Martin & Both]
I really can't stay
(Get over that old out)
Baby, it's cold
Baby, it's cold outside
It's a duet. She's being coquettish. It's a cat and mouse courting.
If you are of a victim mentality, and view women drinking with men in intimate settings as the victims of rape, then it's just the ammunition you need.
If you believe people deliberately drink to lower their inhibitions, then it is what everyone has perceived it to be for the last seven decades, romantic.
It probably doesn't carry across generations well. It's hard to imagine it was a hip hop cover with "baby" replaced with "bitch" to be real for today's underserved audiences.