A person heads out for a walk with their mind somewhere else, caught up in their own thoughts. Then the rain arrives and stays, "all the way," so the walk becomes a long, damp stretch of time with nothing to interrupt it. The poem is only a few lines, but it holds a small scene: one person, one route, steady weather.
The most striking moment comes at the end, when the speaker's "old shoes speak." It's a quiet, slightly odd image. Judging by the wording, the shoes might squelch or squeak on wet ground, and the speaker hears this as a kind of voice. That sound pulls attention out of the head and down to the body and the ground. The shoes being old suggests familiarity, like a companion that has walked this way before.
The mood is calm, a little lonely, and gently humorous. The speaker doesn't complain about the rain. They seem to accept it, and even find company in it.