The dog is running through the snow.
A dog is outside.
It only snows outside, so the dog is inevitably outdoors.
exists e1 x1 x2.(n_snow(x2) & n_dog(x1) & through(e1,x2) & Actor(e1,x1) & v_run(e1))
exists s1 x1.(Theme(s1,x1) & a_outside(s1) & n_dog(x1))