mugging their way through snow dogs 
(ROOT (S (VP (VBG mugging) (NP (PRP$ their) (NN way)) (PP (IN through) (NP (NN snow) (NNS dogs))))))
(ROOT (S (VP (VBG ) (NP (PRP$ ) (NN )) (PP (IN ) (NP (NN ) (NNS ))))))