I know there was a change to stop wild horses following you while holding wheat. However, tame horses only follow on the flat e.g. When crossing a river the horse used to follow you to dry land but now they remain in the water and will not take a step up to dry land. Will not follow you on dry land either. Cows and sheep will follow you up and down dale but horses no - they remain on the same level. You have to ride them to make them change level therefore as in river scenario you have to mount them in water.
Edit by @unknown:
Tamed horses, donkeys, & mules WILL follow you when you are holding food, but they will not walk or jump up blocks when following you. This is both different from the behavior of farm animals, and different from Java edition behavior. The tamed horses/donkeys/mules should walk up 1-block-tall heights without any problem, especially since they can scale that distance without even jumping, and do so when wandering.
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To clarify the problem:
Tamed horses, donkeys, & mules WILL follow you when you are holding food, but they will not walk or jump up blocks when following you. This is both different from the behavior of farm animals, and different from Java edition behavior. The tamed horses/donkeys/mules should walk up 1-block-tall heights without any problem, especially since they can scale that distance without even jumping, and do so when wandering.
Revised the title to be more clear.
Sorry SuperGeniusZeb but your comment is confusing. You say they will not walk or jump blocks and then you say they will walk up 1-block-tall heights without a problem. If they should walk up 1 block heights then why, as shown in the picture, would the horse not follow as it is only a single height block to walk up to follow the wheat? That was in version 1.0.0 and they still won't follow you up a 1 block height in version 1.0.1. I created a new game in creative to check it out and the horse still won't walk up a 1 block height. They'll walk down but not up. Therefore, in my experience, they will only follow you on the flat. This is changed behaviour from prior to version 1.
Similar to MCPE-19591 - horses attached to a lead will not walk up a single block height either?
This may something to do with the lag whilst holding a map.