If you're scared, the horse will be scared. Horses are prey animals and react to fear more than any other emotion a human can show. Having ridden arabians spooking horses are nothing new to me.
My gelding is older now so it isn't as much of a problem, but he can still be pretty silly. The best thing is that when he's in a new situation I ride him with heels firmly down, seat firmly down, and both legs against him, but not necessarily putting pressure on him. It gives him security to know that I'm there for him, and also if he does spook I can quickly keep my seat and apply leg pressure appropriately. I don't change how I hold the reins too much, but then again I'm a ride with seat and leg person. It is a good idea though to keep a light but firm contact and close and loosen your fingers a few times to get the horse's attention and let it know you'er there. If Jazz gets stressed out or alarmed, I talk to him and stroke him from his poll down to his withers, even as I'm riding sometimes. If you're a new rider I don't recommend multi tasking though.
Jazz went from being a show horse that lived and was ridden almost exclusively indoors to being an all around horse that I can ride all over. The first times I tried to take him out into a field it was a disaster. No matter what I did, he'd turn tail and bolt. Finally what I had to do for him was to let him stand still and look and pet him. Then as he advanced forward, if he tried to spin and turn around I'd do one of two things. I would either allow him to spin but keep him in the turn until he'd done a 360 and then stop him so that he was facing the same point. What I found to be more effective than that was to back him into places that he didn't want to go. If you think about it, when you're on a horse and trying to get it to go somewhere, you have the power to steer it left and right and to check it back with your hands. You can urge it foward all you want with hand and leg techniques, but you cannot force it to go forward. You can force it to go backwards. I'd back him up a few steps so that he realized that it was OK as he was still not being eaten, and that like it or not he was going, and then turn him around. Pretty soon he figured it out and just went forward in most cases. That having been said, once Jazz learned to be ridden in the field he loved it, but there was one particular spot that he just would not go. No matter what. One day I got so exasperated that I decided to get off and stand next to him and lead him through it first. When I got off and took a look around, I realized that there was a snake hole, and he and I both got the heck out! Sometimes when you're out in the field you do have to listen to their instincts, but that can quickly get out of control ie "oh he's scared to go over there, must be a bad idea." But in general if you've taught the horse not to be spooky and there's still one thing that it insists upon shying away from, it might be worth it to check out what's going on. It's true that they can sense danger when we cannot.
Also, if the horse ever does bolt, which hopefully he won't, don't shout and don't pull back hard with both hands. I've done both and believe me they only magnify the situation. Shouting only riles the horse up, and if you pull back evenly with both hands, the horse will likely take the bit in its teeth and pull against you, continuting to move and even speeding up possibly. Instead, put more pressure on one hand than the other so that the horse starts to go in a circle. Keep doing this and the size of the circle will decrease and ultimately the horse will slow. BUT if you are inexperienced turning too sharply can cause you to lose your seat, so don't yank - just stay calm.
One more thing. Your safety matters the most. If things are going south when you're riding and you feel like it might be dangerous, stop the horse and get off. If you're in a situation that's dangerous with the horse, leave. It's true that the horse will learn that you stop riding when it does x, but this reinforcement is far more desirable than injuring yourself or the horse. It's not worth putting yourself at risk. I've ridden some crazy horses and never been hurt and done quite well on these horses, BUT if I could do it again, I might not take the risk. True I rode high strung show horses that were freshly broke and never fell off or was otherwise injured, but as I look back I realize all of the close calls I've taken that really weren't worth it. Leave it to a professional if you're really having trouble. It's better to put the horse in a field and never be able to ride it again than it is to be gravely injured as can happen so easily with horses. Back in my horse showing days I was never injured, but within the local show circuit one girl had been killed and another had been life flighted out. Both situations the girls were just not paying proper attention and stayed on the horse and kept pushing it just out of pride and to show off.