A man sits across a table from a woman he is falling for, and the poem catches him in the middle of it. He admires her bare neck while they eat, a small, quiet detail that tells us how closely he is looking. Then comes a gentle mismatch: she loves horses, and he is "in pain from riding." We can read that literally, as if he has gone along with her passion and is paying for it, or as a joke about how stiff and out of practice he is at keeping up with someone else's world.
The last two stanzas turn inward. He calls his past "a very orderly life," which sounds safe but a little empty. Then he worries a cook might find his heart "too old and hard," like a piece of tough meat. The mood is tender, funny, and a bit rueful. He wants love, but he is unsure whether he is still soft enough to be taken in.