The horse has a day that is his and only his, which is not our real time. How his day passes is up to you. What time is it for your horse? You can tell by the history found in the bottom middle of the page on which you take care of him. So, his day starts at 8:00am when he wakes up, and should end whenever you can't do any more actions, or when you should put him to bed, which is 20:00 Howrse
Time. Note that each action you make him do takes up a certain amount of time. For example, meals last 30 minutes, and snacks last 15 minutes.

Your horse must have gone to bed before midnight Howrse Time. After this, your horse cannot do any more actions. The smartest thing, to keep him in shape, is to make him go to bed at 10pm at the latest, which is 20:00 Howrse Time.
When your horse is done with his day, you have to put him to bed. To do this, you can choose between leaving him in the meadow and putting him in his box. The choice is yours depending on the weather on Howrse. Don't leave him in the pasture if the temperature is less than 10C°, for there is no shelter, and don't stuff him in his box when it is above 10C°, for he will get restless and hot.
You don't need to put foals which are with their mother to bed. They go to sleep when their mother is put to bed for the night. When you get your first horse, its mother is Gaia, so it doesn't need to be put to bed at all. That should make you think about looking after each of them very well. Also, when a foal is below 6 months old, it doesn't have a “Put Your Horse to Sleep” button.
Once your little foal has gone to sleep for the night, you must make him age. When he wakes up, a brand new day begins for him. Horses age in 2 month periods. If you use the water of youth, your horse will age month by month instead of 2 months a day.
To make a horse age without waiting until the next day, you need to have aging points. There is a great chance that you will find some during the actions you do with your horse. If you do find one, it will be in the history. Otherwise, you can take 5 points with a pass.
You can also buy Morpheus's arms on the black market and give them to a horse. Your horse will then be able to age when you want. Unlike aging points, however, they cannot be used on just any horse. They are given to one horse in particular and stay on that horse even when they die.
If don't have any more aging points in stock, then your horse will age automatically every day at night at 9am, French Time. You should think of putting him to bed for the night before logging off. Note that if you have not made your horse do anything, then he will not age at night. This means that when you do not log on and play, your horse will not get older.
At of the age of 25, your horse ages and begins to lose his health as well as his skills. The philosopher's stone, which makes your horse immortal, protects the horse against these things as well as makes him live forever. If you look after your horse well, he can live to a maximum age of 35, before he dies and is sent to Horse's Heaven. There is a plus side to this. You gain a pass for every horse over 30 that you send to Horse's Heaven.