Is a quarter horse a warmblood horse?

Quarter horses' temperaments vary; it is not a breed with an easily predictable temperament. Some quarters (particularly older ones) are very quiet and make ideal trail or pleasure riding horses, but there are a lot of working quarter horses and competition horses who should only be ridden by an experienced horseperson. You would need to evaluate the temperament based on what the horse's owner says, or by trying the particular horse you're interested in.