All animals- even humans- can naturally sense a change in the weather and the possibility of a hot day or a storm, because whether we are consciously aware of it or not, our bodies react to humidity.
Additionally, have you never heard the term 'smelling that it's going to snow'? Humans (again, whether we are consciously aware of it of not) notice the difference in the smell of weather (related to how particles are moving in the atmosphere & temperature).
Farm animals- especially cows- can naturally predict the weather and farmers have relied on them for eons. Cows become restless and bad tempered when rain is coming and they lie down when a wet or cold spell is coming (to save a dry spot: to conserve heat. because a cow loses heat standing up).
Insects can also predict the weather. Ever noticed how butterflies disappear before a storm?
As for cats oversleeping when it's going to be a rainy day, I can absolutely say this is not true! Cats sleep for around 16 hours a day and it would be hard to tell if a cat overslept. It also depends on the cat. Some cats hate rainy weather and if it's raining, they won't go out and will just sleep all day. Some cats don't give a sh!t about the rain and will wake up and go out regardless.