hi , i know this is an old post, but can help as this came up in the search engines.
if river mullet it does depend on now muddy things get, but grey mullet are salt water fish which means they will always head to the ocean on outgoing tides and back up river on the incoming. they should never be really too muddy but if concerned let them sit in clean salt water for a while, the best way to make sure mullet taste good in any circumstance is to gut them quickly and keep them clean.
they do better with a cool smoke as they are an oily fish they don't dry out in a slow smoke and taste better this way. hot smokes are faster and more a cooking of the meat with smoke flavour than a true smoke which penetrates better and firms up the flesh.
you back split mullet for smoking rather than gut splitting them. they hang well this way if you have a hanging set up but laid down is still fine, always skin side down. never remove the skin of a fish you are going to smoke, it doesn't just hold them together it helps them to stay moist.
using plain table salt, or seasoned salt but not iodised salt you generously cover the flesh side of the mullet, you leave it salted and covered in a fridge for at least 4 hours and up to 12 this means you can salt at night and smoke the next day. you can sugar and spice flavour your mullet in the last few hours before actually putting them in the smoker, pressing not rubbing brown sugar with any flavours, chilli, morrocan, etc already mixed with the sugar onto the flesh, you can do this at the start but it melts and you lose most of your mixture with the moisture leaving the fish, it reallhy does taste best to do this a bit later and no more than an hour or two before the smoking when much of the fluid is already reduced. (this is a standard recipe for any fish although they are not all backsplit)
Brining is a great way for smoking also:: you create a heavy concentration of salt to water and sit the backsplit or fillets of mullet (or any fish) and make sure they are completely immersed in the brine. adjust the recipe to quantities of fish ALL fillets need to be immersed for a minimum of 4 hours best overnight 8-12 hours. once bought out of the brine you leave the fish to dry before smoking at this point you can add your own flavours if you like
1/2 cup sugar (white or brown)
1/2 sea salt, plain salt ... NON-iodized
1 l water
lastly and most simple is you can smoke fish with nothing added including salt, it keeps better with salt and it smokes nicer but it is not a necessity in the modern day of smoke and eat. xx enjoy