Sometimes it’s obvious, other times it is a bit of a head scratcher. Here are some basic pointers, but always remember to talk to a pet expert if you are at all unsure about what to do.
With cats, it largely depends on their claws and whether they are the right breed. Ragdoll cats, for example, generally should not be taken outside except under supervision, not only because they have historically been bred as house cats, but because they are valuable enough that someone may well make off with it, given the chance. The same goes for things like Bengals. European Shorthairs, Russian Blues, Maine Coons or American Bobtails, however, have the opposite problem in that they generally prefer to preside over a large territory, and so keeping them indoors is not a good idea. Cats which are kept indoors need to be kept thoroughly stimulated, with plenty of opportunities to climb and jump.
Most dogs above a certain size, specifically any larger than toy dogs such as Chihuahuas or Pugs, should never be kept inside all day every day, as they will a) go stir crazy and turn all that pent up energy against your furniture, and b) will suffer health problems due to a lack of exercise. Looking after a dog is a little like looking after a child full of sugar that never grows up. Not all dogs are equal either when it comes to their need for mental stimulation, Border Collies in particular are renowned for their intelligence, one of the main reasons they’re often used as sheep dogs. Of course, like children, the more intelligent the animal, the more difficult it is to keep up with, and the easier it will be for it to get bored very quickly.
This is often a matter of size. Reptiles are cold blooded, meaning they cannot create and maintain their own core temperature like mammals and birds can, and so whether they are ever taken outside depends entirely on the weather; they also prefer environments with very specific humidity levels. Very small rodents, like Hamsters and Gerbils, should rarely if ever be taken outside, as they can very easily get lost; such rodents also prefer to burrow, as open spaces are associated with predators and as turtles https://turtlecaring.com/how-long-can-a-red-eared-slider-go-without-food/. With Rabbits and Guinea Pigs, however, the opposite is true, if anything they prefer to run about, provided there is a safe place to hop to when needed. Make sure your fence is thick and the foundations run deep, however, as rabbits have a habit of digging underneath them. Companies providing decking and fence Springfield IL and elsewhere can provide various options here.
It should probably go without saying that horses should never be kept indoors unless that indoors is a well provisioned stable fit for purpose. Horses like to roam and are generally unfazed by the weather (with appropriate cover put on or available). That said, horses are flight animals, and may bolt and inadvertently cause themselves harm if frightened. Therefore, ideally, there should be some kind of stable facility to store one’s horses, particularly in bad weather like storms or when fireworks are likely.