Keep it under your hat.
Play your cards close to your chest.
Don't let the cat out of the bag.
That's not an idiom. Keeping a matter secret means not letting anyone know about it.
It means you have a guilty secret. Just imagine if you had a dead body in your closet. You wouldn't want anyone to know it. If someone has a 'skeleton in their closet' it means that they have a secret from their past that they are hiding. a shameful and shocking secret that people try to keep hidden
It means things which occur in secret.
This is not an idiom - it means exactly what it says. You should stay fit and healthy.
it means that
It means stay with the rest of the group.
It means " keep calm, don't get worked up"
This is not really an idiom. Baying is a continuous barking by hounds. To keep something at bay means to prevent its escape by surrounding it with barking dogs, or by extension, to prevent a problem from getting out of control by maintaining constant vigilance.
"Keep your hair on" could refer to the Old West, when Indians might scalp you if you were not watchful. I've never heard it said as "keep your hair on" though.I suppose the idiom 'keep your hair on' means that if when a person is stressed the likelyhood that you could lose your hair or even pull it out hence keep it on and keep yourself calmThis may be a mixed idiom - more common is "keep your hat on" which is also means keep calm and don't "blow your top"."Keep your hair on" is advice telling someone to keep calm and not to over-react or get angry.
This is not an idiom. When you compare two things by saying one is the other, it is a metaphor. It means that however you keep your house reflects your personality, and vice versa.
keep it under the hat
It means to be quiet. It also means to keep a secret, such as: "We need to keep that secret hush hush."