The かの is a compound particle of question-marker か and の. Best I can figure is that the か is somehow makes the conjecture into a noun clause. The speaker is putting a lot of conjecture based on the evidence at hand to make a statement of conjecture (even if implausible).
In the example sentence a translation might be "When it becomes April and it starts snowing or something, it's almost as if (you think has) winter come back(?)."