"This year's summer's cold" - though I don't know if Duo accepts that one already.
I think so, yeah. This sentence is purely German style. In English you could say "This year the summer is cold" or "The summer is cold this year", but in German only the latter option of these two is correct along with the given one "Dieses Jahr ist der Sommer kalt" (for one has to maintain the verb's second position) which sounds counter-intuitive for an English-ear as you certainly wouldn't say "This year is the summer cold" in English.
I think it is a little bit confusing because the accusative form of "das Jahr" is the same as the nominative form. I'd rather say "In diesem Jahr ist der Sommer kalt." It's grammatically too. And in that case, when the accusative and the nominative form of a noun is the same, we have to use only the subject-predicate-objekt word order.
I would have thought, "Dieses Jahr ist dem Sommer kalt", just like in "Es ist mir kalt" the "mir" is in dative.
No beacause with the sentence "Dieses Jahr ist dem Sommer kalt" is like you say that "The summer feels cold"(like the summer is a person) and not "The summer is cold".
It seems like it's asking a question 'This year is the summer cold' - but it's not.
In hindsight it's easy to tell because there isn't a question mark, but is there a way to tell that doesn't rely on that?