I just wrote you the most beautiful thing and I lost connection.
Anyway, here's a much shorter thing:
Rhythm = the hoofbeats within one stride. Each beat should get the same amount of time. Such as in walk 1..2..3..4, not ...12....34.
Tempo=how many (full, complete) strides in a minute. 'too fast a tempo' looks fast, tense, nervous, jerky. 'Too slow a tempo' looks like a death march. buzzards are circling overhead. Judges are dying of old age. your trainer is calling a priest to give the last rites - to your horse
. Husband is calling, 'Maaaaaary, when are ya comin' hoooome????'
Cadence=Impulsion+Rhythm (that very, very slight 'pause' where the horse seems to just hang in the air during trot or anter).
Just to make you more miserable, I'll add a few things:
At the upper levels, riders and horses tend to have rather quick, energetic looking tempos. That's ok!
At the upper levels, judges constantly warn riders not to 'over-cadence' the trot. Too much cadence
is not right either! But for most of us ordinary folk, we are always looking for more, not trying to get rid of too much!!!!
(st Christopher is the patron saint of impulsion and cadence, so if you need to pray, he's the dude).