Is it correct to say "the ice"?

Sure. "The" can be used when talking about anything specific. So it is proper to say things like "the water", or "the ice".

Thanks, Theocracy. So, it can be said about a specific piece of ice, not about ice in general?

Yes, you would say "the ice" whenever you were talking about specific ice in a specific place or situation, then of course, in a later utterance "the ice" would imply the before-said particular.

e.g. "The ice in the pond", "The ice in a reaction", "The ice in the freezer".

I see, thanks.

The reason this sounds strange is that if you say "the ice", it means specific ice, so the implication is that some ice is not cold. That's why this sentence feels like an English mistake.

However, as a general statement without "the", "ice is cold" would be used the same way you might say "fire is hot."

I see, thanks. But that kind of weirdness is not related to English or any other language. It's rather a logical mistake, than a language mistake in my opinion.