Because there is so little to the poem—just a few lines, just a few words—the style is essential to its meaning and its effect. The core element of the style is the personification. The fog is made animate, willful, and familiar, by making it into a cat. This implies many other meanings that Sandburg skillfully leaves unsaid. For example, any little trailing wisp of fog can now be seen as the cat's tail, or as a bit of fur left behind. The simple vocabulary makes it accessible; the brief lines give a regular pacing to it.
The fog comeson little cat feet.
The second stanza furthers this metaphor, doubling the first stanza in length as specific catlike qualities are attributed to the fog.
It sits lookingover harbor and cityon silent haunchesand then moves on.
One of the greatest qualities of poetry is to help the reader see things in new ways. One would not typically see fog as similar to a cat, but Sandburg's connection is valid. The qualities attributed to fog are similar to those of a cat, and the poem uses soft sounds, such as alliteration or approximate rhyme ("s" in the second stanza), to further the connection by making the poem as subtle and unobtrusive as the fog he writes about.