With the new ranchers joining us, they aren't quite up to speed with how the Animal Hospital works. Note the Animal Hospital is often simply referred to as "the Vet", "Vet" or "Vetting" your animals. These are all the Animal Hospital that they are referring to.
When you get your starter pack, you need to go to the Animal Hospital and have the Vet "treat" all of them that show up at the vet. If they don't show up in the list then they don't need to see the Vet and are at their maximum health level.
When you birth animals, go to the Animal Hospital and "send all". Usually it's just the mothers who needs to see the vet but occasionally an offspring may show up as well.
If you Race your animals be sure to Vet them at the Animal Hospital before their next race, or there is a possibility they might die during the next race, as racing often uses up part of their condition, how much depends on race length, the animal's stamina, track surface and probably a few more factors. And if condition goes to 0 during a race the animal will die.
Start out running shorter races if you can and note how much the condition has dropped when you go to the Vet, if it only drops a little or not at all then a longer race should be safe. If it has lost over half of it's Condition then you should not race it in any longer races.
Illness works in a similar fashion, if your animals are overcrowded they may get ill, it's called "overcrowditis" and it also reduces the Condition over time, and if left untreated the Condition may drop to 0, and if it goes to 0 they die.
If any of your animals are ill there will be a green "L" in their pasture listing, at the right side of the page.
Illness won't effect an overcrowded pasture until the person who owns the pasture is logged in. This was implemented to prevent animals from dying when someone was not logged into the ranch for a few days. Also it is random if the animals actually get ill, there's a 1 in 10 chance for each animal in an overcrowded pasture to become ill from overcrowding when the system checks for overcrowded pastures. So there is a chance that only 1 or 2 will become ill and there is also the chance that 10-20 or more could become ill.
If your animal has an L for "ill", it needs to go to the Animal Hospital, but also more importantly, you need to reduce the number of animals in your Pastures or add more acres to your Pasture, otherwise after an animal is cured if it is not moved from the overcrowded pasture it may become ill again.
Remember to take your animals to the Animal Hospital BEFORE you DNA them.
I will check at the Animal Hospital from time to time, just in case I forgot to send animals. But anytime you have an animal that shows up, it needs you to have the vet check it.