Yep, it's kindof a fine line between cautious/aware and nervous and for a first time trainer, the line gets blurred. Relax and try not to be nervous because the horses will feel it. However, don't let your guard down even for one second cause they can feel that too and some horses will take advantage. That is something that has to be learned in time; how to be cautious without being scared, and how to be alert and ready without being jumpy. Relax but stay alert.
You said you were planning on riding one of them today. Did you get it done and if so, how did it go?