The poem is only a few lines long, but it moves quickly from the ordinary to the strange. The first couplet is plain and almost confessional: when the weather is dry, the speaker reaches for wine. "Dry" can mean literal drought, but it also hints at an emptier, parched inner state, so the title, "Thirsty," starts to sound like a longing for more than a drink.
Then the poem turns. The "secret owl of my heart" is "married to a swan." An owl suggests night, hiddenness and watchfulness, while a swan suggests grace, light and water. The speaker seems to hold two very different sides of themselves, one private and shadowy, the other elegant and open, joined in an odd union. Judging by the imagery, the wine may be a way of coaxing that hidden self out, or of soothing the dryness between them.
The mood is quiet, wistful and a little playful. It feels intimate, like a secret spoken aloud.