I think you should ride however the horse is most reassured. I personally ride with loose reins all the time; however, I will keep them a bit shorter on green, spooky, or broncy horses. I like them short enough that I don't have to make a lot of adjustment when something happens. There is a method that I just recently learned for dealing with spooky horses and I have found that it will work wonders.
As opposed to re-writing it, I am just copying and pasting and I added just a little bit more:
whenever they spook and move their feet, tighten them down into a tiny little circle almost like a one-rein stop but keep leg on them and keep them moving in that little tiny circle. It will sometimes feel like they are about to fall over and you will get dizzy but just keep them going. If they start getting sluggish, bump them a little bit with inside leg, outside leg, or both. Even bump them with a leg back onto their flanks or up onto their shoulder, that will help them to realize that you aren't going to kill them when you move a leg around a bit. Then when you are ready to stop (not them, you), switch sides and turn them in tiny circles the other direction with leg or bumping to keep them going. If he starts laying on your hand, just give him a little bump with the bit to get him off the bridle and don't stop turning a direction until you like where his head stays. If you do this every time he spooks and jumps, it is amazing how quickly he will quit finding ordinary things that he wants to be afraid of. Do this throughout the entirety of your ride. If he sees something scary, let him look at it so long as he doesn't move his feet but if he jumps or starts to bolt, start the circles all over again. You can drain the piss and vinegar out of any horse in 10 or 15 minutes of doing this and they seem to be less spooky and more attentive when they can't get enough oxygen. I used this on the little Arab gelding that I rode and the difference from one day to the next was like night and day.