This doesn't refer to tying a horse to a tree. Tying-up, otherwise known as azoturia and "Monday morning disease" is a condition found in working and athletic horses.
Tying-up is a symptom rather than a disease. It refers to extreme muscle cramps and soreness that horses sometimes demonstrate after a rest day.
Any horse can "tie up" if exercised beyond its current fitness level. This is often seen in hunters at the start of the season or endurance/serious trail horses in the spring.
Some horses, however, do it regularly. It's associated with two diseases:
1. Recurrent exertional rhabdomyolysis is a defect in muscle contraction that's more common in anxious horses and in females. It's an inherited condition (so horses with RER should not be bred).
2. Polysaccharide storage myopathy is most common in Quarter horses, and is caused by glucose being cleared from the blood too quickly, which puts too much glycogen in the muscles.
An episode is treated by giving fluids and possibly sedatives, then putting the horse in a large stall or small pen where it can move freely, followed by a gradual return to exercise.
Chronic cases are managed by lots of turnout, avoiding rest days as much as possible (and making sure the horse stays out if it has to be rested.
Acute "Monday morning disease" is a good way to incapacitate a horse (without doing long-term damage, as long as it's given plenty of water).