OK, I reluctantly accept that the "open" button has gone and clicking [...]
while on a horse opens the horses inventory, not the players, is as designed.
per MCPE-18242.
I get that this aligns with console etc versions.

However, there should then be a hotbar area in the horses UI to enable the player to manage the hotbar contents as in pc/console version?
Currently on MCPE, the only way is to dismount any time you need to use an inventory item which is not currently in the hotbar.
This sucks the fun out exploring/mapping on horseback IMHO.