I'm not sure how other yards introduce newcomers into a herd but here we use a 'socialisation' paddock.
It's a small fenced area beside the field that the new boy or girl will be going into and where they stay for a week or so.
From this paddock all the horses are able to see one another, sniff and touch over the fence and all the squealing is dispensed with in relative safety.
We observe the behaviour of the newcomer and the herd when they interact to try and identify any potential problems or potential fieldmates. This time of socialisation, we find, gives the newcomer some idea of it's place in the hieracy and generally reduces the drama when the newcomer is finally introduced into the herd.
The socialisation paddock also gives the owner a chance to get to know the other horses and gives them a period of 'settling in' as well.
Happy owners make horses happy!!!