Driving is driving when you're talking about this kind of basic stuff. Besides, you won't be showing under AMHR or A rules with your girls anyway!
As for how to train your animal to go forward on voice, it's a matter of teaching them what the cue means and rewarding them when they do it, just like any other training. When you tell them to "get up there" or "trot on" or whatever cue you plan to use to mean "add impulsion to your gait" you have to insist they at least make some sort of effort and calmly escalate your request if they don't.
Example: I ask the green horse to Trot and he raises his head and walks a little faster but doesn't trot. I'm going to keep careful contact on my reins (rather than throwing them away and allowing the animal to go on its forehand), re-collect him or her, then ask again for the trot in a firmer tone of voice. If she doesn't trot I'm immediately going to flick the animal with the whip on the back near the saddle area and ask again. Most of them will give up and pick up a trot at this point and I'm going to slightly soften my rein and praise the horse verbally for the correct response then allow him to walk again after a few good strides. If giving in to your request only gets them more work, they're going to be reluctant to do it. They need to know that doing the right thing is both easy and brings things they like such as a chance to walk or stand again.
When you first ask your horse to trot faster or offer a lengthened trot (which aren't the same thing) they won't be able to hold it for more than a stride or two because they simply won't have the muscle yet. As long as they give you at least an effort to move out you reward them, but they really must give you at least an effort or you'll ask again more firmly. Letting them get away with ignoring you sets a bad precedent.
That's really all there is to it...the rest is just building it a few strides at a time until the horse can hold the gait or speed as long as you ask. Take it slowly, be on the lookout for fatigue or soreness, and look for little things to reward so you always end on a good note.
As for blinders, no, they aren't absolutely necessary. Many organizations require them so I think it's important that every driving animal learn to go in them but if you prefer to drive "open" (without blinders) and your girls are happy and safe that way you certainly can. I'm not completely comfortable until I know they can drive either way, it's just one of those safety things for me. I use blinders because I show but want that horse to know what's behind him as well.
Leia