I'm just impressed you've observed so many different kinds of body language in such a short time! I think that you'll be figuring out their language really quickly!
While there are some fairly universal body language cues, some are really specific to the horse and/or the situation. I agree with BlindHorse that pawing is generally about frustration, but really, many signals can mean different things. Take nickering. It can be a sign of interest or curiosity. It is very often anticipation (like they see a person and figure they might be getting fed or getting out of their stalls), but it can also be a sign of distress, like when you separate a horse from its herd, or a special buddy (yes, horses form bonds with other specific horses). Some horses nicker all the time, like my gelding, who is just very vocal. Some almost never do.
Ears back can also mean a lot of things. My gelding does it to show annoyance. My mare does not - if she does it, it's generally submission to my gelding who is the boss.
Snorting is usually a sign of extreme curiosity and high alertness in my experience. My horse will do it on a trail if he spots a deer. It's like he's saying what the heck is that and why is it there, is it going to hurt me? It might be done in the context of a new person in the barn I suppose.
If a horse puts his head towards you, I'd resist the urge to pet just yet, especially not on the muzzle. But you can let them smell you, like you would with a dog (but not with an open palm, because they might think there's a treat in there). They're sniffing you. Trying to figure you out. In my experience, few horses really like to "cuddle". They're not like dogs at all. However, once you get to know them individually, and they get to know you, you can figure out what they like. My mare loves a scratch between the eyes. My gelding doesn't like to be touched on the face, but likes a good neck scratch. Usually, I scratch rather than pet them though. I will say that my gelding does tolerate me hugging his head. But he didn't always. I think that he understands that to me, it's a nice feeling to "hug" him, so he leans into me a little. He would never seek it out, but he "allows" me to do it, like it's a special privilege, LOL.
My mare was shy and anxious when she first came to us, but she was very curious. I spent a lot of time just hanging around her, and she eventually started coming over to smell me, then started letting me scratch her.
The bottom line is that while horses have their own body language, there isn't an exact equivalent for every "sign". Think of a dog barking. Some do it in aggression, some in excitement, some bark a lot, and some not at all. There's really no way to generalize. You just have to get to know them. After you've been around them for some time, you will develop a sense of what the horse is trying to tell you, and be able to respond. Keep observing! But don't push too hard. Remember, they are prey animals, unlike dogs.