Confirmed on Minecraft 1.7.10 on Java 1.7.0_45, Windows 7 x86_64.
On opening a single player game to LAN, the host sees all skins correctly but to other players, the host appears with the default "Steve" skin.
The last version which did not exhibit this bug appears to be Minecraft 1.7.4.
I can confirm that this bug still exists on Minecraft 1.8.3, Windows 7 x86_64.