The speaker wants to be courted, and the first lines sound like a classic Valentine's wish list: dinner, wine, being known, being made a Valentine. The rhymes and sing-song rhythm of "Dine me, wine me" give those lines a playful, flirtatious bounce, almost like a little chant.
Then the last lines bring everything down to earth. After all the grand romantic gestures, what the speaker actually asks for is "a spoonful of honey / for my cold." The shift is funny, and it's also tender. Romance here isn't only candlelight and champagne; it's someone looking after you when you're sniffly and run down.
The title helps set the mood. February is cold and bleak, and the cold in the final line echoes that. The tone stays light and teasing, but there's real longing underneath: to be pleasured, understood, and cared for in small, ordinary ways. The poem suggests the speaker may care more about comfort than glamour.