OP - congratulations!
I sympathise. There is nothing more off putting than being "reminded" about sex by OH. It should come naturally, otherwise it is just another chore.
Now a chid is like a bombshell physically and emotionally. A nice one but still, it does change a lot. It is normal to feel confused. What you wrote made me wonder; has his life changed at all?
Its sounds like you are tired, baby focused, which is normal. What is he now doing that he was not doing before? Is he simply waiting horny on the sofa for your to finish BFing baby? Is he sleeping soundly while you have broken nights?
I find my DH much more attractive and sexy when I am rested and feel that he is working as hard as I am. have you spoken to him about this?
What you said about wanting intimacy first, kissing, talking, holding, before resuming sex is very pertinent too. Is he trying to take it on board?
Breast milk takes 90 minutes to digest they say, so he could take baby for a walk or drive, given the cold, while you sleep.
BFing is not a get out card for dads. For example as soon as DD1 use sleep, my DH would send me to bed, close the bedroom door so that I would sleep on and sing/rock baby when she woke as long as possible so that I could rest before the next feed.