I'm absolutely nothing of an authority on this, but since no one else has replied & I'm in a similar boat to you, thought I'd reply with the way I'm going about it...
Firstly, if your horse is only 3yo, I wouldn't personally be asking much of it under saddle or in harness for a while, physically speaking. However, I think that it's best to go slow & thoroughly, especially where driving is concerned, because being a bit more 'remote' on the back of a buggy, I think it can be potentially more dangerous than riding if things go wrong. Therefore, if the horse has very little education at all yet, you probably have a way to go before physical work comes into it anyway.
I don't know what your 3yo has learned, so I'll start at the start; I would ensure it can *calmly* yield to pressure in any manner, forwards, backwards, hind or forequarters and that it is desensitised, calm & accepting in a wide variety of environments & situations. *I think a calm, well adjusted horse is even more important for driving as for riding.
As for specific driving training, I hadn't ever ground driven my horses before I started(tho they were used to my online control & with young kids I'd also taught them to be 'led' from beside), so that's where I started. First in a controlled environment, then out & about. I ensured they were very calm & understanding of all that before I 'muddied the waters' with further factors.
Then I harnessed them, but before attaching anything to them, I started with just me hanging my weight off a rope attached to both sides of the breastplate. That way, if things got out of hand, I just dropped the rope or lessened my weight. As my horses had learned so thoroughly to yield to light pressure, it was actually amusing the first few lessons, getting through to them that they could actually go forward while I was hanging off the breastplate! I also got them used to strange things 'chasing' them with me as the 'safety chain'. That is, I ground drove them while I dragged something like a tyre or barrel or such. That way, there was no risk of them running off with something chasing & further terrifying them. They weren't attached to it until they were already used to moving into pressure and having wierd & wonderful things behind them. When I first did attach these things, it was by a quick release knot that I had hold of, so in the event of upset, it would release the knot when they startled. Thankfully my prior preparation must have been OK because nothing ever came of any of that.
Then I made a couple of 'training shafts', just out of a couple of light saplings and 2 cross pieces. The horses were already used to things against their sides, backing into confined spaces, etc. Again when I first used these I put the ends in the tugs but didn't attach them to anything, so if worst came to worse, the horse would just pull away & they would fall from the tugs. I started ground driving with the shafts with me holding them up, then when I deemed it safe to attach them, I did, again with a quick release that I held and let them drag it around. I also then attached the training shafts to the 'britching', so they got the idea about backing with pressure on their hind ends too.
So... that's all been going great and I figure the next step is to hook them up to a light cart, but I figured with my lack of experience, I'm going to find someone experienced in driving & training to instruct me, or at least give me more practice before I take my boys to the next step. Just haven't gotten around to that yet though.
Hope that helps you & hope others reply with their tips... pref those with far more experience than us!