Just take the puppy out, plop her in the snow/ice whatever…..if they have any brains they learn quickly to hurry up. That's what's great about the winter, teaches them to not to take more than a second or two.
Sometimes we get double negative degree temperatures here, I'm sure NY does too.....a little cold won't kill them....and 30 degrees sounds pretty typical.
Unrelatedly, I would force her to wear the booties....get used to feet handling while she's still tiny. I don't think I could have predicted how many foot injuries I would have had to treat - and I hear people all the time saying "rover won't let us touch his feet...so we have to take him to the vet and have them do it."
They have disposable, waterproof rubber booties (brand is called PAWZ) they may come in her size. I love them because they are very tight, and hard for a dog to grip onto, easy to wash if they get peed on....plus they are disposable, so if she breaks one there's 11 others in the box that can be used...instead of having to buy a whole new set. If you get the right size they can't shake them off.