What's the difference between さむい and さむく?
さむい is the original dictionary form - い adjective, just like あつい hot, おおい many,あかい red, しろい white
さむく is used to join verbs in a sentence, after swapping い withく
さむくない turns it into a negative form.
Wouldn't "samui desu ne" be a bit more literal translation for "isn't it cold?"
Why is the "-ku nai" necessary?
At a guess I would assume the ね is rhetorical whereas this is more of an actual question.
寒いですね is more of "It's cold, right?" while 寒くないですか is more of "Isn't it cold?" the same way we would say "Isn't it cold?" in English, when it is very cold and we expect the person we're talking to to agree with us.
Why is 寒くないですか？not correct?
It is, report it.
how do you ask, "It's not cold, isn't it?"