When I am buying a horse I always advertise the price as the horses are in the range of $1,000 to $10,000 which is within the most common price ranges and also the most price sensitive price range. I.e. someone who will pay $5,000 for a horse may not even consider a horse that is $7,500 so it is good to be clear so that you attract people who are willing to pay the price you want (in a general sense of course, negotiation takes over eventually).
Horses over $20,000 you will often find $POA because 1.) Buyers who are willing to spend that kind of money often have a broader range i.e. they may be looking from $20,000 to $50,000 and be less price sensitive. 2.) Sellers who are looking for bigger money will often have a wider range of prices they will accept i.e. they may advertise at $40,000 but would accept $30,000 to the right home. So at the higher price ranges there can be greater variation between advertised price and accepted price.
When I am looking to buy a horse I am looking in the lower price range and never look at ads that do not have the price displayed as there are literally thousands of ads to look at so I would be on to the next ad without even batting an eyelid.
All horses deserve, at least once in their lives, to be loved by a little girl.