how difficult is it to place former racehorses in new positions?

Sometimes it is very hard. A typical horse is trained not just commands and such but they are taught manners as well. Don't stomp on feet, no biting, no cribbing, etc. An average horse begins training, slowly, while still a foal. First wearing a halter, and being led, and being handled in general, then tolerating things like farriers, clipper, horse trailers, and equipment like saddles and bridles. The horse is almost always very used to these things, and 3-5 years old before a human ever gets up on their backs, at which point there's more training.

Race horses are thrown into training after their official first birthday on January 1st. They are fast tracked through everything, barely taught how to deal with human, often they have a person on their back before they are even legally two. Race horses are taught two primary things; to break from a gate and to run like hell.

Once you get a racehorse off the track it often has no manners, no real training, and a very strong instinct to bolt every time there's a rider in the saddle. Because of their delicacy and cost racehorses are almost never ridden unless they are being toned up for a race or unless they are in a race. So now all of a sudden it's like starting all over again. You have to teach them not to run away. You have to teach them control, collection, pacing, in many cases you have to teach them how to relax.

Thoroughbreds are fantastic horses and can be flexible. Some horses are like my rott, in that they are so pleased to interact with a rider that they really want to catch on fast. Some, even most, like a challenge, like physical activity and like stimulation. But some never want to give up the foul tempers. Some are soured on people, possibly from abuse, possibly from negligence, some are just plain mean.

It's always a challenge to retrain a racer, sometimes it's just easier with one horse rather than another.