It would be better to say _The sky being clear is a sign of the night being cold_, or a condition of it.
For, as Mill says, the essence of a Hypothetical is to state that one clause of it (the indicative) may be inferred from the other (the conditional).

Similarly, we might write: _Proof of Joe Smith's not being a prophet is a proof of his being an impostor_.
This turning of Conditionals into Categoricals is called a Change of Relation; and the process may be reversed: _All the wise are virtuous_ may be written, _If any man is wise he is virtuous_; or, again, _Either a man is not-wise or he is virtuous_.

But the categorical form is usually the simplest.
If, then, as substitutes for the corresponding conditionals, categoricals are formally adequate, though sometimes inelegant, it may be urged that Logic has nothing to do with elegance; or that, at any rate, the chief elegance of science is economy, and that therefore, for scientific purposes, whatever we may write further about conditionals must be an ugly excrescence.

The scientific purpose of Logic is to assign the conditions of proof.

Can we, then, in the conditional form prove anything that cannot be proved in the categorical?
Or does a conditional require to be itself proved by any method not applicable to the Categorical?
If not, why go on with the discussion of Conditionals?
For all laws of Nature, however stated, are essentially categorical.