What does Cole’s crushing of the caterpillar indicate about his personality, even in his beaten state?

I think that there are a couple of things at play here. Although beaten into a pulp and bleeding profusely, Cole crushes the caterpillar. He still has plenty of anger and fight left in him. Cole is a headstrong kid with a lot of rage in reserve. This also describes Cole's loss of domination and control. The Spirit bear was not afraid and pretty much had his way with Cole. Cole felt powerless against the bear and needed to impose his control on something, anything. The caterpillar was the only thing available.