Lauren at She Moved to Texas wrote a really excellent post about the glut of free horses on the market - and on the people looking for those free horses. Spoiler alert: unrealistic expectations abound.
I've worked at several different horse rescues over the years. The last one I was most involved in was the place where I got Tristan. He wasn't really a free horses - but he is pretty darn close. I paid a discounted $150 adoption fee for him after working there for 3.5 months. He was no picnic - but he was a far more straightforward case than many horses at the rescue.
Here's what I have to say. *pulls up soapbox*
The #1 best thing you can do for your horse, to ensure his longterm success and happiness, is to train him.
I don't necessarily mean every horse should be a steady eddy packer cleaning up the ribbons. I do mean that every horse should have basic manners, basic skills, and a decent outlook and disposition. They should consent to be handled by a variety of people, and they should be accepting of bridle, saddle, and basic aids.
Will your horse go better for you, or for a talented rider? Sure. Almost certainly. But can you put a middling rider up on them and have them at least go okay? Can you hand his lead rope off to someone with minimal horse experience and trust that he will more or less behave?
Horses end up in bad situations for an endless, depressing, variety of reasons. Horses get out of bad situations, often, because they are good citizens. If you're looking at the rank, untrained 20 year old horse lined up next to the relatively chill 20 year old who's had basic training...guess which horse is going to get adopted? pulled out of the feed lot? spoken up for by someone trying to place them?
So take your time. Take the extra 5 minutes when handling your horse to make sure that they have the basics down. Ask a friend to handle or ride your horse just to make sure he will be okay with it. Try him out in a lesson or two with a stranger. The more you can expand his mind and add to his experiences, the better off he'll be in case something happens to you.
(soapbox corollary: have a plan for your animals if something happens to you! but that is the subject of another blog post entirely.)