My friend and I both have Minecraft version 1.10.2, and we play together all the time on a LAN server. When I host the world we like to play in, I open it to LAN with survival, cheats on. When my friend joins, I can see their skin on their player. But when my friend shows me my player on their screen, I am the default Alex skin. This makes me very sad as I spent much time custom designing my skin. I have also tried changing to a different skin off the skindex and that didn't work either. I think its a LAN host issue because when my friend hosts, I can't see their skin but they can see my skin when I join their LAN server. I do hope this gets fixed soon! As far I can tell from google reports, this has been happening since Minecraft version 1.8.