Yes, I agree with the comments above. One really big advantage is that
there is so much of it out there! If you're using food indoors, you have to be careful as otherwise it's all gone in 2 mins and there's the clearup to think about. Outdoors in the mud, you can go bonkers in it and there's always more available! Result!
On the downside, clean-up can be an arse to avoid getting it all over the inside of the car for the journey home.
The way I used to do it was to take my mountain bike out, with me dressed in cycle gear and carrying my sploshing outfit in a carrier bag over the handlebars. I'd go to my fave spot - an especially quaggy and secluded bridle path in the middle of nowhere that was pretty much unused as it was unpassably quaggy on foot. I'd then change into my outfit and have my fun then wash off as much as possible in the large puddles before changing back into the cycle gear again, carrying the muddy clothes back in the plastic carrier bag they arrived in.
Sadly, the council drained and hardcored that bridlepath a couple of years ago and I haven't found a suitable replacement yet.
I know some people go barefoot in the mud but I don't think that's sensible as there can be sharp things in it. Soft clay is definitely the best as it is smooth and spreads beautifully, giving superb coverage and retains the moisture (and, hence, its viscosity) extraordinarily well. Ordinary top-soil type mud isn't much good for clothes or tights filling as the water just drains out straight away and you're left with just coarse sand in there which can be irritating!!
I find that the best is where you get wide and deep tractor ruts that fill with water in areas where there are alluvial deposits near rivers on flood plains etc. If you stand in those, you can scoop out the soft clay with the tiniest particles that is always the last to settle under the water. You can get a huge handful of lovely soft sloppy clay which is ideal for dropping into panties, tights or throwing up the inside of a skirt (or just smearing). The water in the ruts comes in handy later for the clean off.
Of course, you need to be careful which type of field you're in if you want to make sure it's just clay and mud and not something a lot more unpleasant if cows have been around. (Urrgh! - OK, I know some of you are into that but it's a major turnoff for me and probably most others!)
I'm guessing that rivers that are far enough inland not to be tidal (but not so far inland as to be fast flowing and, thus, not depositing clay) won't have the oyster problem but you need to be careful with rivers as they are often used to 'carry stuff out to sea' and you don't want to be ingesting any of that, unless you like the idea of having your stomach pumped! (Notice how many chemical plants are alongside rivers as well as the obvious sewage farms. Heavy metals and untreated sewage can both be extremely injurious to health!)
You can use Google Earth to search and zoom in on likely looking places. I wish they'd get a licence to show the geology info from the British Geological Survey too as that would be very handy. (You can get maps from them but they're a bit specialist and, therefore, pricey, so I haven't done so yet.)
If you want to try it indoors, you can get clay from
PotClays. I usually use 1150 Modelling clay as it's very plastic and mixes to a gorgeous grey/white emulsion. If treated carefully, you can scoop up 70% of what you use into a bucket for re-use. (You need to do that to avoid blocking the drains anyway!) That also makes it very economical.
Hope that helps.