Preparing for Kiddush, I felt cold and put on a non Shabbos hat in less than a minute (the hat was very close to me) and continued to prepare for Kiddush. Did I break Shabbos?
If I understand you correctly you mean to say that you put your weekday hat on instead of your Shabbos one. Although it is correct to wear Special Shabbos clothes, if it wasn’t done, we will not call that breaking the Shabbos. You missed out on this way of honoring the Shabbos but it isn’t as if you violated the Shabbos by doing one of the 39 melachos.