There are no rulebook-specified ways of holding the reins in either mini breed registry-not even in the ADS. Like others, though, I feel that a two-handed hold works best if each rein enters the bottom of the corresponding hand, either under the little finger or under the ring finger, and exits 'over' the first finger, with the thumb resting lightly but firmly upon said rein-similar to the 'ice cream cone' hold we used to use when riding with romal reins. It is also possible, with practice, to allow the rein to come unto the hand under the little finger and exit between the first and the middle finger. This frees the first finger and thumb to hold the whip. You simply can't have nearly as light a touch, as much sensitivity, IMO, when the reins come into the TOP of the hand and exit out the bottom. Not sure what you meant by 'hold them in a loop', kaykay? If you meant those literal loops that attach to the reins-I would say absolutely NOT! All those do is make the driver "haul on" a horse's mouth-maybe on the trotting/pacing track, but otherwise--not for me! There are ways of 'bridging' the reins that can be very effective;you aren't likely to see that in a breed show ring, but that wouldn't preclude you from learning how to use it well, along with one or more reinholds common in the breed show ring. There CAN be more than one acceptable and workable approach! I also recommend training the horse to, and maintaining, light but firm contact, bending on the corners, etc.-which, with competent driving judges, should stand you in good stead wherever you show-for that matter, wherever you drive!
I have to add that I have observed that most miniature horse breed show ring drivers in no way utilize the whip,much less properly(I believe that the AMHA rules, at least, no longer even require it to be in the driver's hand, but only 'in the vehicle'....which is idiotic, IMO)--now, as has happened before, someone may well LEAP to point out, 'this is not the ADS"--and you're ONLY too right, it ISN'T(thank goodness!)....and since how horses are driven in the breed show ring, at least minis, is a very different situation from the 'wider' world of driving-then no, I am NOT saying that they can really be compared---BUT, speaking from personal experience( I STARTED in the miniature breed show ring-and with success--and have "moved on" to a more ADS-orientation of driving)-no matter where, and why, you drive, you will NOT go wrong by learning and practicing the proper (and amazingly successful,WHEN proper!) use of the driving whip! The BEST way to do that is to learn to drive one-handed-but THAT takes dedication and practice, and isn't easy.
What I am saying is that you can learn to do a good job in both a show ring style AND a "wider world" style, to both you and your horse's benefit, IF you care to study and learn, and work at it. Certainly lightness and sensitivity,along with consistence of cues, are ALWAYS of prime importance!
Margo