I don't know if this group is still active but I did find a web reference and an email address. I know they've gone "silent mode" but maybe have resurrected anew.
http://show-me-naturist.tripod.com/showmenaturist/index.html
If they are around they're centered around Columbia and if you make contact you'll likley learn of some swimming holes. There have been some mentioned in the past that were popular with Columbia and MU folks. One was a quarry site near Eldon - nice place that I've visited several t imes but not recently and it's on private property - not a public venue.
Also you've likely heard of Show Me Acres - a great resort development near Stover, MO. That is a going venture with regular members -mostly couples but the owners will explain their policies if you make contact.
http://www.aanrmidwest.com/showme/
They might be able to put you in touch with others in your area - could take a few email exchanges but I'd guess there are some streams or lakes that'll be what you're looking for.
If you learn that the first group - Show Me Naturists - is active would you email me or post it here. I think we've taken them off the list of active Missouri groups but perhaps they are indeed up and running.
Good luck - where there's a will there's a way - to get some sun.
Dick in KC