I dotnt think that post horses woudl be badly treated eiether, as they were meant to be able to go fast and horses need careful handling and treatment to be at hte best of health. That's why one had to change horses during a journey, to get fresh ones. (If you only had a pair of horses, they had to be rested and fed durign a long journey)
And yes, I think its clear that the horses on a visit, were put in the stables of the house, (as Emma says to Mr Woodhouse the horses will be in Mr Weston's stable while they are visiting the Westons), and only called for when they were ready to go.