It's pretty simple. If you ride against ladders/vines you'll still go up. I'm not completely sure if this is a bug but it doesn't seem intended.
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If horses shouldn't be able climb ladders, then slimes, creepers, magma cubes, ocelots, wolves, pigs, sheep, chickens, etc shouldn't be able to climb ladders either. (RIP most slime farms)
@Toraby I think it was all mobs except for squids, bats, ghasts and maybe blazes. Basically all flying mobs 😛
Most, if not all, mobs can climb ladders, even if they don't have hands. It seems particularly silly with horses because they're so big.