2024 PHB rules are that it does damage to every creature according to the amount of movement through the sphere, so it wouldn’t stop the horse directly; sufficient damage would impose the Dead condition on the horse and reduce its movement to zero feet (or maybe it would willingly stop at 5’)
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If the horse is moved against its will, the rider makes a DC10 (ie. fairly easy unless one is clumsy/impaired) saving throw to avoid being thrown off though
I would expect a higher DC if it’s eg. a druid using Thorn Whip out of nowhere, but a giant grappling the horse or something? That’s typically not so sneaky