This is a bug that has been severely plaguing LAN play since the skin server was updated during the 1.7 line. The host of a LAN world always appears with the default skin to all who join. However, the host can see their OWN skin correctly and there are no issues with the skins of any other players. Confirmed for the latest Operating Systems and on the most up to date build of Java.

Note: This bug has been fixed by default in Minecraft Forge, indicating that it can be fixed via code on the client-side without further modification of the skin server.