Of course, God cares about animals! He created them!
Look at what Jesus says when he talks about people and how we worry.
Matthew 6:26-
"Look at the birds of the air, for they neither sow nor reap nor gather into barns; yet your heavenly Father feeds them. Are you not of more value than they? Which of you by worrying can add one cubit to his stature? So why do you worry about clothing? Consider the lilies of the field, how they grow; they neither toil nor spin; and yet I say to you that even Solomon in all his glory was not arrayed like one of these. Now if God so clothes the grass of the field, which today is, and tomorrow is thrown into the oven, will He not much more clothe you, O you of little faith?"
God cares about all of His creation, not just us. But creatures, unlike us, do only what God created them for. They do not worry like we do, because they know they will be taken care of. Yes, I do agree that we are to be good stewards of animals and the rest of the natural world.