Various issues that can come up:
Milk/meat mixtures: Pet food does not have to be kosher, but it cannot have milk/meat cooked together.
Pesach: You cannot feed your animals chometz on Pesach.
Shabbos: Pets may be muktzeh on Shabbos. Consult your LOR. You may also have issues with trapping animals*.
Spaying/neutering: This could also be a potential problem. Contact your LOR.
The Wolf
* Many years ago, some of our hamsters escaped on Shabbos and had the run of the apartment until Shabbos was over. It was actually quite fun watching one of them climb the steps in our apartment. 🙂