Thanks for the additional information everyone.
Equinegirl, as far as I'm aware, she didn't try to bite or nip at all. I don't recall her head coming back toward me. That said, it's not something I was looking for either, and being new I may not have recognized it if it did happen. I'll keep that in mind today as I have another lesson. I watched a few videos and will be prepared to flap my elbow if her head comes my way. (yes?)
Horsesdontlie, yes, much more similar to that than a biting/aggressive reaction. It was very quick. As I remember it, probably on 12-15 "clicks" of her hooves on the floor altogether. (So maybe 4-5 steps leftish, 3-4 to the right, and 3-4 back to the left). It wasn't as pronounced as what your horse did, but the overall impression was one of sagging and staggering under too much weight. That is what it "looked" like. I think though from the trainer's explanation that it was anxiety about the pressure of the girth. (Or I may have misunderstood or relayed her explanation incorrectly). Oh, also, I think her head was up -- kind of stretching upward. Overall it was short lived, and likely more dramatic to me than it would ha been to a more experienced person, though there was deffinately something going on.
My thoughts are that today I will be concious of watching for her face coming toward me or other signs or displeasure/aggression. I will also make sure I'm going slowly with the girth. I wonder if maybe last week I went more quickly than I usually do as I'm becoming more proficient at tacking up and don't have to talk myself through each step. I'll also be sure to ask for help if I begin to feel uncertain at any point while brushing and tacking her up.
I don't want anyone to think my instructor is not attentive. Part of what I like so much about her approach is that I am allowed to come early and get the horse ready myself, rather than having her all tacked up when I get there and then just hopping on for a lesson. I love that I get to spend time brushing her and smelling her and all that good stuff. My trainer has slowly given me more space to enjoy this time. She is always available, and makes trips down the aisle for other reasons (though I'm sure it's partly just to check on me). There is another girl who works with her as well, who is usually doing something with another horse at the other end of the aisle. She is always available to help he, and I think keeps a loose eye on me as well. It's just a fluke that I was alone in the aisle when it happened.
Other than this, very easy pony for me to deal with as a beginner. I can get her when she's in her paddock -- she just stands there. She stands nicely for brushing and feet. She puts up with my poor riding. ; ) Takes the bit extremely easily. (I am supervised directly for this). I don't want to give the impression that I am with some aggressive, poorly trained horse. I did tell the trainer what happened. Other students ride her as well, so if it was a pain issue I'm sure they will have discovered it by now, and if it's something that has continued she will be aware and will be working to address it. I do think she's very thorough and very safety minded. : )