It depends on the horse. I like to ride them a little bit in the beginning to assess what I’ve got-- are they relaxed or spooky, are they strong or weak, stiff or wiggly? I want the horse to realize he has a new job, not racing. But he also needs down time to be a horse, heal any minor injuries (muscle soreness), and get a mental break. For some horses this is a month in the field, basically left alone; others do better with more interaction and some light riding.
Once I have established that the horse can stop, go, and steer reliably, it’s time to hit the trails. Lots of hacking, no drilling in the arena. Working on circles with a young 3 year old is pretty pointless; they get bored and they aren’t strong enough to accomplish much anyway, they’re likely to be unbalanced, still growing, and it’s unfair to expect much. Get out and see the sights, experience terrain, water, wildlife, and new places outside the ring. Go to horse shows, tie to the trailer and walk around. Go hacking with a buddy at first, and then alone if he’s settled. Keep it low key, mostly walking and jogging. The frequency depends on the horse and my time, anywhere from once to several times per week.
Late in the year (Nov/Dec) I might start to do a little more flatwork. Big loopy circles, learning canter leads (perhaps only on the straight, no circles if really unbalanced), and introducing turn on the forehand and leg yield at the walk. Walking and trotting poles. If things are going well I might hop over an X or tiny log to judge the horse’s willingness and aptitude toward fences. The form may be sloppy at this point, but it’s more about how the horse reacts to the obstacle: does he naturally grasp the concept of going over? Is he confused or scared? Does he rush, or slow down to figure it out?
Then give him time off over winter, no major work just hacking if anything. Start in the spring as 4 year old with “real” flatwork concepts and introduce jumping as the horse is straighter and stronger.
It’s good to have an older riding horse so that your three year old can be “forgotten” sometimes. If that’s all you have to ride, it’s tempting to do too much, especially if the horse is talented and willing. Keep reminding yourself he’s only 3, he has a long life ahead of him to do big exciting things. At this age it’s just important to develop a calm, willing attitude that will be the foundation for the rest of his career.