The title gives the first clue: "anadromous" describes fish, like salmon or shad, that live in the sea but swim up rivers to spawn. So the "fish that come in May" are travelers returning home, and the poem treats their deaths as something close to a human loss. Calling it a "funeral" is a striking choice, and the word "hard" suggests the grief is heavy, maybe even difficult to watch or to bear.
The last line shifts from observing to acting. The speaker says "I must keep one in ice," which sounds like a duty or a compulsion. Judging by the wording, the speaker may want to preserve a body as proof, a memory, or a kind of private memorial. The word "must" hints at urgency, as if letting every fish vanish would be a betrayal.
The mood is quiet, spare, and solemn. With so few words, the poem leaves a lot of silence around its feeling, and the cold image of ice makes the mourning feel both tender and stark.