Ix-nay on the 3/4 time.
A horse has three footfall-beats and a pause-of-suspension beat in a canter...which makes for FOUR beats in time (three sounded, one unsounded 'rest' beat), so you will have to have an up-tempo piece in 4/4 time, though a 6/8 can also work.
A waltz will get out of time.
Good point. Just figured I do sing Row your Boat which works, and is 3/4 time.
Each horse is different. I had one the Timid Freida from the musicalJaques Brele is Alive and Well and Living in Paris worked. My current mare likes Lady Gaga songs. And I had one that I had to count... singing never worked on her.
Being a huge Beatles fan, I like "With a Little Help From My Friends", especially if I want to slow my horse's canter down. Something about the song just feels canter-y to me. "Eight Days a Week" I like for a bit of a faster pace.
Row, Row Row Your Boat isn't in 3/4, it's in 6/8. At least, I learned it that way- if you search the sheetmusic you will find it in 3/4, 4/4 and 6/8. It still works for a canter, because you can divide it into a 'base four'.
I love listening to the recommended songs! Especially 'Pump It'.
I often find myself singing (or thinking) the song I Can't Decide by the Scissors Sisters. The rhythm works for my mare, and the lyrics are very...let's say truthful for some of our more interesting rides! Let's just say I only sing it when mares and I are having a difference of opinion. Boys Round Here might work too. Also maybe Hey Jude by the Beatles?