All are grammatically correct, but #1 is not used for the same purpose as #2 and #3.
For example, #2 is 2 points. Then what about #1? If a boy writes #1, how would you grade the problem? One point or no point?
I’d give it no point.
No, sentence #1 is not grammatically correct. The definite article "the" is necessary in this sentence to make it grammatically correct. In English, we use "the" before a noun to indicate that we are referring to a specific noun or something that has already been mentioned or is known to both the speaker and the listener. In this case, since we are referring to a specific weather condition (in this case, the cold weather), we need to use "the" before "weather". Thus, sentence #2 or sentence #3, both including the definite article "the," would be grammatically correct.