It is an inverse statement, which is not necessarily true. It is one of the laws of logic and logical reasoning.
What makes it illogical is:
From a logic point of view, then YES, the second statement you give is always true (regardless of the temperature outside); this is the weird logic of "implies" (→)
A B →
T T T
T F F
F T T
F F T
If the first statement A (it is snowing) is true, then the overall truth of the sentence (if it is snowing then it is cold outside) is based on the truth of the second statement B (it is cold outside).
However, if the first statement A is false (ie it is not snowing) then the statement "if it is snowing then it is cold outside) is true regardless of whether it is cold outside or not.
All you are told is the state of the temperature if it is snowing; if it is not snowing then no determination of the state of the temperature can be made.
It is the logic of implies that is the downfall of many mathematical proofs: if ANY step is false, then you can prove anything you like. For example you can prove that 1 = 2 by employing the false step of dividing two different things by zero (though it is often hidden within algebra).
The sentence you give as its negation is not the logical inverse. The logical inverse is "If it is not cold outside then it is not snowing" - as you know that it is true that it is cold if it is snowing, then if it is not cold then it cannot be snowing must be also be true (otherwise if it was not cold and it was snowing, then is it not true that if it is snowing then it is cold).
This sentence also agrees with the inability to infer temperature if it is not slowing as if it is cold (statement A being false) then whether or not it is snowing (statement B), the sentence is true - you have no ability to infer the falling of snow if it is cold:
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No, it's not always true because it could be below freezing with no snow falling. It rarely snows in Antarctica, it just appears to be because of all the snow being blown around, but it is still very cold there.
no it is NOT true, it can be too cold to snow.
True or false? You can rely solely upon induction to prove that your conclusion is correct.
The converse of the statement 'If it is snowing, then it is your birthday is 'If it is my birthday, then it is snowing.'
If it is my birthday, then it is snowing.
If it is not snowing, then Paul does not wear a sweater.
To negate "It is snowing and classes are cancelled" make the statement negative: "It is not snowing and classes are not cancelled."
Yes
Alice was upset that it was snowing outside because she had planned to go for a hike that day. The snow made it difficult for her to go out and enjoy the outdoors as she had intended.
if you are wight you can not get coghut you can blind in
Yes, but because of the introductory clause, we add a comma after 'snowing.' Therefore, the sentence becomes this: "Although it was snowing, he walked home." Then it's grammatically correct.
because it was snowing outside
She'd like to go swimming, but it's snowing outside.
Not sure what you are asking but if it is snowing outside then yes you can say it is snow.