so-called Wobbler Syndrome means the horse has a neurological problem, a malformation of the channel that the spinal cord runs through so that parts of bone are pressing on the spinal cord. (The term is sometimes used more broadly to include the same result acquired as a result of injury. And there is at least one infectious disease, EPM, that can produce vaguely similar effects).
So, nerve impulses do not travel properly down the spine to some of the nerves, generally the hind end being most severely affected. The horse is weak and wobbly back there and 'does not know what the hind end is doing'. Mild cases may not be noticeable until/unless the horse is spooked, required to turn sharply, or asked to carry a rider; moderate cases may have an unusual gait or not be able to move beyond a staggering walk, prefer to lean against a wall or fence when standing, and fall or lurch dangerously into objects with frequent injuries; severe cases may not be able to stand or walk.
It pains me to tell youthis but it does not generally improve (there are a few exceptions but do not hold your breath, and when there are improvements, they are generally mild at best). Sometimes it gets worse or sometimes it stays the same as the horse gets older. I know there have been attempts to alleviate it surgically (on some race-bred TBs) but my impression as of ten years ago was that it didn't really do a lot of good and was fiercely expensive.
I have known mild to moderate Wobbler cases kept as pasture pets, but quite honestly they did not do all that well in the long run in most cases. Most horse pastures and stalls are just not safely enough built to have a horse that lurches around or trips or doesn't always know what the back half is doing, and they tend to be prone to painful and expensive injuries.
Sorry, but if the colt cannot even stand, then there is really not likely to be any happy future for him. And horses do spectacularly poorly as nonambulatory patients, they just can't survive without being able to get up and walk around most of the day, pneumonia or colic or infection sets in and it's a painful death unless you step in and do something about it.
Big hug,
Pat