You'll have to run the skipTime or setDate command on the server as well. Not sure if setDate is local or global though, but skipTime is local and thus only changed on the machine that runs the command.
One way to get around the troubles of broadcasting commands across the network could be
createUnit a gameLogic with the skipTime command in its init line.
If you want to set the time at mission start you can simply process the setDate or skipTime in the init.sqf outside of any isServer or isPlayer checks.