Great question, Tidy Rabbit!
I tend to think of "hot" as short-hand -- when someone is in a hurry and not going to go into particulars about a horse's temperament, in one word you can provide a lot of insight about the animal, and get a good indication of what kind of rider might or might not like him.
Many people would call my horse hot. I might call my horse hot. But only if I needed a quick one-word description. To really describe him, I would call him quirky, sensitive (most of the time), over-reactive (sometimes), and even lazy (sometimes). Excessive - can be. Full of himself - usually. Bundle of energy? often. Spooky - sometimes. But when he's good, he's like a hot fudge sundae with whipped cream and the cherry on top.
TR, I can totally see why someone would call your horse hot, especially someone who definitely doesn't want a "hot" horse. For those of us in love with our sometimes excessive, flamboyant, spooky, or quirky beasts, we think up lots of adjectives to better describe their big personalities :)