So until they fix this one (assuming they ever do), the best workaround I've found is to create a resource pack with the host's custom skin in place of alex.png (and or steve).
However, since all other players joining the host's LAN game will need to use this resource pack, it's only really practical if a small/consistent group is playing.
@Logan Who
The trick is to create a resource pack that has your skin in place of the Alex/Steve skin, and then have your friends that are playing over LAN use said resource pack.