First of all, congrats on doing things the right way.....ie taking lessons to get yourself knowledgable and prepared for the horse world. You have no idea how many beginners just run out and buy random horses with little to no help, so you are starting out the smart way!
Second, welcome to the fall months, when many of our normally lovely horses are full of beans. Most horses are more energetic and even spookier when th weather is crisp, and add a brisk wind and wheeeeee....they seem to kind of get high on it, so you are not alone.
I handle the fall sillies by doing a few things, some of which have been suggested already, but I just want to clarify how I do it.
If you can, start with some ground work- ask for control of all body parts. Disengage hindquarters, backing up, moving shoulders and head away from you, both directions. Longing in smaller circles at just a walk or trot with frequent changes of direction. Clinton Anderson's "longing for respect" video is a great one to watch to learn how to do this.
Then, after I am mounted,
1-I try to really put the horse to work, immediately. Start with asking for lateral flexion both sides, several times, then ask for some disengagements of the hindquarters in both directions. Next, if you feel safe to do so, ask for some vertical fexion and then a nice back up. Not too long, maybe 5-6 steps, the release, praise, and move on.
2-If I had good results with number 1 type stuff, then we start moving around more, start walking, but ask for shoulders to move over, make small circles and serpentines. Change your direction frequently because it keeps the horse focused on you "What the heck is she going to ask me to do next here?"
3- Basically start doing number 2 at a jog/trot. If at any time you start to feel out of control, disengage those hindquarters. It will get control back of the horse, reinforce you as leader, and it is something you almost can't practice too much because it is something that eventually needs to come naturally to you in am emergency.
4-Relaxation of *my* body. Horses are amazingly sensitive to tension. When I am asking my horse to really focus on work as listed above, I do try to keep my breathing rhythmic and steady. If I am going out on the trail, or if I am trying to get a relaxed easy walk in the ring, and my horse is feeling silly, I put myself into *total* relaxation mode. It will seem counterintuitive to you at first. Instinctively, we riders want to tense up on a horse that is getting hyper. We want to clutch hard on those reins in an attempt to gain control. That reaction, however, will send all your tension into your horse and it will just get more and more upset.
So how do you learn to relax when all you want to do is hang on for dear life? It takes practice, and, to be honest, a bit of nerve. I leave, my reins long and loose (if she were to break into a trot I would do a quick 1 rein stop and then put her back on a loose rein again). I let my body go limp amd relaxed.....sack of potatoes. Loose neck, head floppy, arms floppy, lower back soft and following her stride. Long slow deep breaths. And possibly, the most important thing to hep you relax is something called "soft focus". Sally Swift discusses it in "Centered Riding".....a book I think all riders can benefit from.
Soft focus, as I understand it, is basically kind of like blurring your eyes, not focusing on anything in particular. Sometimes to get started, I close my eyes completely. The theory behind soft focus is that, as predators, humans tend to have sharp focus, it is something that a predator will use to lock onto prey. It causes tension in the body that the horse can feel, and having a soft focus will greatly relax your body and your horse. There are plenty of times that I don't use soft focus, for example if I am picking a certian point I want to head my horse towards, and she feels that too. But if you are trying to relax yourself and your horse, soft focus should help.
Hopefully some of that will be helpful, these are things that have worked for me with excited horses in my riding life. My current mare will actually drop her head, sigh, lick her lips, all signs of relaxation, if I just do the relaxation stuff described above.