So let's tell the story again, with explanations.
In the tale the order of appearance is backwards, first the pig which tells us when we are in the story. We are well in spring. Then the wolf appears with the frost, he can't get into the pig's house, because it would mean turning back time, this is why he enters backwards, but it proves to be a dead end... in a bag. The pig with the warm rains of May "scalds" the wolf, basically turning back him into a dog (pushing back him in the calendar), reminding him of his place. The pig flees up to the tree, which is safe since wolves can't climb trees. Interesting, pigs can't either, but he is capable. Why? How? The tree is the Tree of Life or World Tree, which is nothing else but the Milky Way. The position of the Taurus zodiac is such, that it reaches into the Milky Way. This is how the pig can climb up, but since the Aries with the wolf is further away, it can never into it.
Now the wolf brings his buddies (some version says 10 more, which makes the sum of the characters 12, an interesting number if we are talking about the zodiac), and they stand upon each other. This band of wolves together represent a different kind of myhtic monster, the griffin. Little known fact that double headed eagles (for example in CoA but the iconography goes back the the ancient Middle East) are griffins. And when the wolves stand in each others' necks they have to balance out by standing towards opposite directions making the pile "double" headed (looking one way and the other). A griffin's body also a carnivore mammal (these days we call it a lion, but for example in Sumerian lions essentially were called dogs, or at least they use the same cuneiform to them, and in historical time they knew little about Linné and his system).
Then the pig have to remind the wolf to it's place again (go into your own house DOG!), to get free from the chilly biting of the remnants of winter (wolves and their hunger are typically associated with winter).