Hi and welcome!
Good mini conformation is just like good regular horse conformation only tiny.
It is definitely hard with the fluff, it makes them all look obese and short-legged! Here's a few things I personally looked for when searching for a driving mini. There are some really knowledgeable breeders on here who will hopefully chime in with other things I didn't think of.
I paid particular attention to the feet and areas where abnormal fat pads would form if the pony were actively IR. So I wanted nice solid feet without any visible dishing on the toes (aside from normal flaring from lack of trimming) or big ridges that might indicate past laminitis, and no cresty neck or fat pads along the sides and around the tail head. If the horse is badly IR, exercise will only do so much and there are a lot of management issues that come along with it to keep laminitis at bay. My horse is still young and he may develop IR at a later time but it's much easier to prevent it from causing a problem than to manage the problems if they have already happened.
I wanted a horse with a nice efficient trot and a strong hind end. I paid attention to the hind leg conformation - minis can be predisposed to stifle issues so that's something I looked for. I ended up with a horse that is somewhat cow-hocked but who engages his hind end and lifts his back naturally when he moves off, whether he's hitched or not. So much easier if that's just there from the get-go rather than having to train it in.
Also, while a downhill conformation would be a hard stop for me with a big horse, I felt it was less important in a driving horse and my horse is slightly downhill although I think he may develop out of it, he's still young and was not in work, and he lifts his front end naturally when he moves. But I still wouldn't want one that is dramatically downhill since I think it makes their work harder for them and predisposes to front leg issues.
For me the most important thing was temperament. I wanted a sensible horse without anxiety, to the degree I could determine that just with a quick introduction. So I took him out on a lead, took him away from his friends and to an area he wouldn't normally go, and watched how he acted. He didn't scream for his friends or get rude and try to drag me back that way. It's proved to be true - if his buddies leave him behind he's fine with it, if I take him out and his neighbor screams for him, he doesn't get bothered by that either. I think that's important in a horse who will be a companion since he might be getting left behind at least some of the time and you don't want to have to be worrying that he's freaking out while you're away. My vet told me when he basically waved a vial of sedation in Rowan's direction and we had to hold him up while his teeth were done, "your pony has very little circulating adrenaline". He can still get up to some trouble but he's not anxious while doing it!
I'm not a very big person and I use a Hyperbike so the total weight my pony has to pull is only about 160lbs, but we do have some hills and rough terrain/muddy areas where I drive so I didn't want him to have to struggle to pull me. I had driven a 35" mini when learning to drive and we zipped around fine in the ring in an easy-entry cart but I felt that a slightly bigger horse would be better for my purposes: Rowan is 37" and solid built. I think this becomes way more important the more off-roading you want to do and the steeper your terrain. If you're mostly going to drive on flat, firm surfaces then just about any mini could pull you fine as long as your cart wasn't too heavy. For me, I wanted to stay well below "full draft" which is when the horse is pulling its own weight. I think my horse weighs about 275#, maybe 300. So if you got a similarly sized mini then you'd need a pretty light cart to stay below full draft. Most of the easy-entry type metal carts are around 120lbs or so. The Hyperbike is only about 35-40lbs.
And FWIW, I used to trim for a woman who had a large mini that was her endurance Arabian's companion and she used to take that pony along on most of her conditioning rides. So they can go pretty fast and far! The pony was still fat, though.
Sorry, that ended up turning into a book! Hopefully it's a bit helpful, at least.