Hi, Yasya, you appear to have successfully answered your own question. In our example, “ice” is uncountable (as it usually is), so it cannot take the indefinite article. It cannot take the definite article either, because it is not definite. Also, if we did use an article or other determiner, it could (depending on the meaning) go before the entire noun phrase “some melting (participle) ice” (= some ice that is melting), as opposed to “melting (gerund) some ice” (= the process whereby someone or something melts some ice). Finally, you are correct that “some” is a partitive, which would be most appropriate if we wanted to emphasis that we’re talking about only part of the ice that exists. To sum up, depending on whether “melting” is a participle or gerund, we could say “some melting ice” or “melting some ice”, which would in practice have about the same meaning as the ambiguous phrase “melting ice”. Let me know if my explanation cleared that up for you or not.

It might be because "to melt the ice" is a famous expression which means to try and create friendliness instead of animosity. So to melt ice literally is an expression which is used without "the" to somehow set apart these two meanings of "to melt (the) ice"..