I think you're getting genuine HR readings.
Don't count on the trot being the way to condition your horse
cardiovascularly, though. There are several factors to be considered--the
most important is "specificity" of muscular exercise. Condition him as you're
going to use him. If that means canter, and if canter means a lower
non-challenging heartrate, then I would canter faster rather than training at
a trot.
ti