I am not sure, but there could be a set expression like this and that's why it could be more correct to say "to smelt ice". i was wondering, what is smelting of ice? melting ice I understand...but what is smelting exactly? TY :D

I assume you mean “melting” (turning into liquid from a solid) not “smelting” (a process for making metal from metal ore). Adding the “the” changes the meaning. With the “the,” it means that YOU are trying to make the ice melt, but you are having a problem and are not successful in making the ice melt. Similar example: “It is too cold in the room, so I’m having a problem melting the ice.” But without the “the”, it means that the problem is that the ice IS melting. “We have a problem with melting ice. Because the polar ice has been melting, sea levels are rising and polar bears are moving south into populated areas.”

First, I think you mean MELTING. Smelting is what you do to metal. You can use "the" = you are talking about a particular ice - e.g. the ice on your windscreen... You can not use "the" = you are talking about ice in general. So, both could be correct - just different contexts. You don't need the "with" in this sentence...

You should use 'the' of you're talking about some ice in particular. Without 'the' it means any ice (a general problem). :)

Thank you!