A sudden cold snap has frozen everything, and the speaker goes out among the icicles, snapping them off. The poem's clever turn is that the sound of this breaking becomes a tune. It's "one-take," like a musician who plays a piece once, live, with no chance to fix mistakes. The icicles can only be broken once, so the music can only happen once.
The speaker seems playful and a little delighted. Instead of just enduring the cold, they treat it as an instrument and make something out of it. The words "breaking" and "snap" give the poem a brittle, crisp feel, and you can almost hear the small, bright cracking and tinkling. There's also a quiet sadness in how fleeting the music is, since each icicle is destroyed to make its note. The mood is clear, sharp, and cheerful, with a hint of the temporary nature of beautiful things.