this is probably a well known issue as the launcher is currently very new, but with a LAN server when another player tries to ride a horse the are kicked off. if they try to get back on they are kicked within a few seconds.
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Duplication of https://mojang.atlassian.net/browse/MC-13736
thank you for showing this to me, i thought it might already be well known.
Ezekiel
Duplicate of MC-13628, please use the search function to see if your bug has already been submitted. Currently over 54% of tickets are being closed as duplicate.