Okay, well let's tear this **** apart, shall we.
(I really can't stay) But, baby, it's cold outside
(I've got to go 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
Okay, first verse, pretty simple. She wants to leave, and he doesn't want her to. This is obviously the first instance where her wishes are refused, it's pretty creepy and sets up the tone of the song. This theme is, and the overall creepiness, is added too by the last line in the stanza, "I'll hold your hands they're just like ice." This brings up the thoughts of a "frigid woman" and his desire for her to losen up. All of this in the context of her clearly stating that she wants to leave.
(My mother will start to 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
(Well, maybe just half a drink more) Put some records on while I pour
Now, this could be where one could make the argument that she really wants it, but is more worried about the societal reaction to her staying with a man as an unmarried woman. With her referencing her mother and father, yet with the stanza that precedes it, that loses some credibility. She said she wants to leave, yet he is not letting her, and like a lot of women who find themselves in a situation like this, they start trying to appeal to any kind of authority that the man would yield too so that she can leave, because the man here has already demonstrated quite well that he doesn't respect the authority she has over herself. Even if she does really wanna stay, yet is saying no because of societal pressure, she has the right to say no because of societal pressure, or any reason she damn wants. People are allowed to have complex emotions, and people are allowed to make choices. She has not given consent in anyway here, and she has clearly made her desire to leave clear, and since she has not given consent, we can not imagine consent. Saying that she really wants to say is akin to saying, "well, she said no, but her eyes said yes!"
(The neighbors might think) Baby, it's bad out there
(Say what's in this drink) No cabs 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
Again, she starts out this verse trying to appeal to someone else's authority, in order to trigger his own response for shame so that she can leave. Her implying that the neighbors might think poorly of the two of them, him especially, is another factor that is driving these appeals to authority. Now, the drink part here is shocking, even as someone else said, it just means that she was noticing the alcohol. Obviously in our minds, a line like, "what's in this drink" brings up images of Bill Cosby, but even if that wasn't the context it is still troubling. Because her surprise by what is in the drink, implies that she wasn't expecting any alcohol. He's just trying to get her drunk, and you can see that with his line, "Your eyes are like starlight now." The twinkling of the eyes implies intoxication, which is what is entire motive is for having another drink.
It's also important to note her last two lines in this stanza, "I wish I knew how To break this spell." This can be read as her starting to blame herself. She is thinking that this guy is so infatuated with her, and if she could only get him to not like her she could get out of here. She's putting this whole situation on her. That it is her responsibility to break down the situation, and that if she can't get out, it's her fault. When in reality, he should just let her out the door and be an adult about the situation. It's kind of amazing how this breaks down into what happens to far too many women.
Continued in part two below.