Don't think having a horse already trained somehow takes the fun or learning out of it. On the contrary, a horse already trained lets you have fun and learn right away.
There is a saying that goes "horses train people, then people train horses." In other words get a good horse to help train you, then after a number of years you can get a horse to train.
Maybe you will be a lot more successful than I am (although horses are my lifelong passion and I haven't stopped learning about them since I was a kid) but I have had horses for about 16 years, and I am only just now training my first one from the ground up. And it's harder than I thought it would be.
But look at it this way, if you get a horse with training you can skip much of the frustration and trouble and actually enjoy the horse (and learn) right away. There will be plenty to learn with even a well broke horse, and you can still do all the groundwork and stuff with them too.
So it's up to you, but almost everyone who has had horses for a while can agree that it's enough of a challenge for a first time owner with even a properly trained horse, much less a horse without training.
Good luck with your search. I would love to own a draft!