How would you suggest that I sew a pouch into a hoodie?

If it's a zip-up, I would make a large fleece square with a mesh window (for ventilation) and a zipper across the top, and sew it on like an inside pocket.
Or you could put it on the outside so the little ones can look out, just depending on what you want.

I make pouches on sweatshirts and I have done some on hoodies also. I have some sweatshirts with some on critterbin right now.

Do I basically make it like a pouch with a zipper and a window?

If I were doing it, yes, sized to fit the hoodie. Just make sure the bottom is pleated or boxed so no one gets squished.

I need to figure out how to box corners.

The black line is the fabric; the blue line is your inside seam; the red line is the seam to box the corners. (I didn't show the zipper or window insets, but that's why it's closed at the top.) After sewing the red line, cut off the excess fabric. This will make a kind of pyramid-shaped pouch; if you want it more squared, you can box the top too. Be sure to allow extra length as each box will shorten the pouch.

Thank you very much.