Cooling Out: What Ten Minutes of Walking Actually Does
The walk at the end of a session is the part most often cut short. Physiologically it is doing more work than the part of the ride that preceded it.

Cooling out is the most skippable part of a session. The work is done, the horse is fine, the evening is going, and ten minutes of walking in circles feels like a formality invented by somebody with more time than you have.
It is not a formality. Of everything that happens in the last quarter of an hour of a session, the walking is the part with the clearest physiological justification.
Exercise does not end when you stop
At the end of a hard piece of work, a horse's body is in a very different state from its resting one. Heart rate is elevated. Blood has been redirected toward working muscle. Body temperature is up, and the systems that shed heat, sweating and increased respiration, are running hard.
None of that resolves the instant you halt. It resolves over the following minutes, and how you spend those minutes determines how smoothly it happens.
Walking keeps the circulation working while the body sorts itself out
During exercise, a large volume of blood is moving through the muscles of the limbs. Stopping abruptly asks that circulation to slow down at exactly the moment the body still needs it moving, to carry heat away from the muscle and to clear the by-products that hard work generates.
Walking solves this without any effort on the horse's part. It keeps the limbs moving and the circulation cycling, at an intensity low enough that the horse is genuinely recovering rather than continuing to work. Heart rate comes down gradually instead of dropping off a cliff. Heat continues to move out of the muscle and away.
A walk is not a lesser version of exercise. It is the mechanism by which the body transitions out of it.
It also tells you things
A horse that walks out loose and level after hard work is a horse that has coped with the work. A horse that walks out stiff, short, or unwilling has told you something useful, and it has told you at a point where you can still act on it.
This is the second, quieter argument for cooling out. It is the only part of the session where you are watching the horse move at low intensity, unasked, with your attention free. Most owners spot a developing problem during the walk home rather than during the work itself, and that is not a coincidence.
How long, and how
Long enough that the horse's breathing has settled and it feels cool to the touch in the places that hold heat, under the saddle area, between the hind legs, along the neck. On a mild day after moderate work, ten minutes is often enough. After hard work, or in heat and humidity, it takes longer, and the horse decides that, not the clock.
Walk on a long rein. The point is a relaxed, swinging walk with the neck low and free, not a walk held in an outline, which is still work.
Where conditions are hot, walking combines with the other cooling measures rather than replacing them. Getting cold water onto a hot horse moves heat out considerably faster than walking alone, and the two together are better than either.
The part that gets skipped, and why
The reason cooling out gets cut is that its benefits are invisible and its cost is immediate. Ten minutes is ten minutes. Nothing visibly bad happens on the day you skip it.
The effects are cumulative and quiet, in the same way that most things affecting a horse's long term soundness are cumulative and quiet. That is exactly what makes them easy to skip, and exactly why they are worth protecting.