Nobody values a "free" animal. Negotiate the price down if you like the buyer and his/her intentions for your horse.
I'm sorry to hear some people feel that way. That's very shallow!
I got a free horse once, and was on of the best horses I've ever owned. I don't know why anyone would think less of a horse because it's free. The price doesn't make the horse, anymore than paying $10,000 would make a horse a "good" horse.
If it were me, I would use something like "right price to right home." I have seen that wording used before and to me that means the horse is free or cheap to the right person.
Word of mouth is probably the safest bet though.
Really, we should care more about the animal than a couple hundred here or there. Someone might take in a free horse if it has something to offer them but would be turned off by paying for the same horse. In other words, it might persuade someone who is otherwise not looking for a horse but has the room and money to feed another mouth.
Would you pay $500 for a pasture pet? Probably not. But might you take in the same pasture pet for free, if it was perfect for the grandkids or occasional trail ride or something? Maybe a friend-of-a-friend knows the people and that they are looking to find a horse a home? Quite possibly.