Leash for a goat should be tied in holes into its horns, bc if it just around its neck, the leash will easily slip off and the owner may come to carry it in the street. The Gemara is unsure about if the rope tied into its beard.

A cow cannot go out with a strap between its horns. If the strap is for decoration, it is certainly a problem (bc it is unusual to adorn cows and it’s therefore considered a burden). If it’s for protection, to control the cow, it’s really excessive protection and subject to a dispute if excessive protection is considered a burden or not. (Same dispute as the nose ring for camel and leash for a cat form yesterday)

A red heifer is only kosher if it has not performed “work.” Carrying a burden would invalidate it.

A horses collar if it’s easily pulled by the owner is certainly not a burden as the mishna stated. But if it’s jsut wrapped around the neck and hard for the owner to pull, it’s a dispute if the collar is considered a burden. (Rashi holds one opinion is lenient for adornments on animals and tos holds even wrapped around it still provides some protection bc the owner can grab it.)

A persons rings can become tamei. An animals ring cannot (they are not classified as כלים). If a person had a ring and it became tamei, it would remain tamei even if a person started using it for his animal bc no change has been done To the ring. If one performs a physical change to the item, it loses its tumah. (R Yehuda says this is only if the change is destructive)

An item used by people on animals, like a collar leash or a staff that drives animals is considered a kli bc it’s used by people.

A ring used in a belt is so a kli bc it’s an adornment to the garment and not directly for the person.

Only metal rings can become tamei but not wood ones. The only wooden keilim that become tamei are those that have a receptacle.

A sewing needle that was tamei and had its eye broken would lose its tumah (it’s not longer useable for its original function), but a needle made without a hole to be a pin come accept tumah.

On Shabbos a woman is not doing a melocho Doraysa wearing a finger ring. But if she wears a ring with a seal she is liable. A woman who wears a pin isn’t doing doraysa carrying but if she wears a sewing needle with an eye she is carrying.