Irving first establishes a deep connection between his sketch's eponymous protagonist and his dog, Wolf, in order to set the stage for his eventual apprehension:

Rip’s sole domestic adherent was his dog Wolf, who was as much hen-pecked as his master; for Dame Van Winkle regarded them as companions in idleness, and even looked upon Wolf with an evil eye, as the cause of his master’s going so often astray.

Describing Wolf as "Rip's sole domestic adherent" highlights their relationship vis-a-vis "Dame Van Winkle," who thinks that both of them are lazy "companions in idleness." Irving underscores this loyalty by telling the reader that Wolf "was as courageous an animal as ever scoured the woods."

This connection elevates the significance of his initial apprehension regarding the strange people playing in the mountain glen. Upon hearing his name called, Rip begins to approach the men, and

at the same time Wolf bristled up his back, and giving a low growl, skulked to his master’s side, looking fearfully down into the glen. Rip now felt a vague apprehension stealing over him; he looked anxiously in the same direction, and perceived a strange figure slowly toiling up the rocks, and bending under the weight of something he carried on his back.

Because Rip and Wolf are so intertwined in the narration, this "bristl[ing] up his back, and giving a low growl" on the dog's part implies that there is danger ahead for both he and his master. This is why Rip feels "a vague apprehension," which foreshadows the decades-long slumber that is about to befall him after drinking with the strange men in the glen.