How independent are cats?

Last year we bought a house on acreage. I’ve never really been a country girl before.
We have two dogs that are mostly indoor dogs but play outside a lot. We are getting ready to fence an area for them so they can stay in the mud room if we are gone a few hours and can go out their electric doggy door to potty.
We have a bit of a mouse and squirrel problem and I was thinking about adopting a grown cat or two to hang around the house and take care of them.
I don’t want to be cruel but I DO NOT want indoor cats. I am willing to feed them and provide shelter outside for them but I don’t want them in my house.
Am I being cruel to even consider this? Is it better to save a cat from the pound but make it be semi wild or should I just skip the idea?
It does snow up here but I was thinking of providing a shelter similar to a chicken coop with a lightbulb for warmth and blankets.