an asian female with a backpack is snowshoeing with a black dog.
The woman is going snow backpacking with her dog.
The first sentence doesn't make any reference to the female's age confirming she is a woman nor does it imply that the female is backpacking.
exists e1 s1 s2 x1 x2 x3.(with(e1,x3) & n_dog(x3) & a_black(s2) & Theme(s2,x3) & Actor(e1,x1) & v_snowshoe(e1) & with(x1,x2) & n_backpack(x2) & n_female(x1) & a_asian(s1) & Theme(s1,x1))
exists e2 e1 x1 x2 x3.(n_dog(x3) & of(x3,x1) & n_female(x1) & n_woman(x1) & for(e1,e2) & with(e2,x3) & Actor(e2,x1) & v_backpack(e2) & Theme(e1,x2) & Actor(e1,x1) & v_go(e1) & n_snow(x2))