There's a very common myth that horses grow teeth throughout their whole life. That's not true. They grow teeth for the first seven or eight odd years, and then those teeth continue to erupt for the rest of their life, until the root part erupts and there is no tooth left, which is usually between 35 and 40.
The teeth take up a lot of space in the jaw.
Horses have milk teeth and adult teeth.
When they have jaw bumps like this, then it might mean the horse is having trouble losing the infant teeth, and the tooth is growing downwards instead of upwards. You need a dentist to check that out.
You can imagine that the jaw and mouth area would be quite sensitive during this time. This period between two to four years is exactly when we're typically "mouthing" - teaching the horse to become accustomed to having a metal bit in its mouth. This might be something to consider if the horse is reactive to mouthing or bridling while the horse is being started under saddle.
You can read a horse's teeth and determine the age because, while the chewing surface will depend on the diet of the horse, the teeth erupt from the gumline at a predictable rate. You can see the profile of the tooth as it emerges from the gumline. The ridge in the profile of the outermost incisor is referred to as 'Galvayne's groove'.
While it's not an exact science, you can estimate a horse's age by looking at the outer incisor.
Domestic older horses have trouble getting all their calories from pasture, because their incisors often become uneven, which makes it difficult to pluck enough grass to maintain their weight.
Add to that their grinding surface tends to deteriorate also. You will often see much longer stalks of grass in a aged horse's manure. You can help to meet their calorie requirements with softer feeds like copra meal, speedibeet, soy hulls, or bran (wheat and rice bran is not suitable for horses with insulin resistance or Cushings), and by feeding precut pasture in the form of chaffs. It's important to thoroughly wet the feed into a mash.
For very old horses like the one pictured above, you may need to supply all of their calories, ideally in several meals a day. Calorie requirements will change over seasons. They will typically need more feed in winter. The best way to decide how much to feed is to continuously monitor body condition. In younger horses we will watch for condition over their ribs, but geriatric horses can often have some ribs showing even if they are a healthy weight. Another option is to monitor 'thigh gap'. If condition in the hind quarter is dropping then it is a good time to perhaps add another meal into the day.