Attempting to get a Mule through a nether portal is problematic. sometimes the mule will successfully go through the portal and other times it will not.

the problem seems to occur in both the nether and overworld with a chest equipped mule with or without a saddle. As with horses the mule cannot ever go through a portal while mounted. but this problem occurs both when pushing a mule into a portal or dragging it through with a lead.

the only work around i have been able to find (for both overworld and nether) is to walk so far away from the mule and the portal that the chunks are removed from memory, then walk back so the chunks reload. usually that will "reset" the mule/portal and the mule will then be able to pass through the portal. however, i was surprised to discover that the same workaround did not happen by relogging or passing through the portal on foot and then back again.

this is happening on a SMP server. i have not attempted to duplicate the issue in single player.