To add to what others have said, look at an AT tyre: it has big knobbly blocks that are good in SOFT terrain (mud, soft sand), or thick soft snow (we don’t really get that in the UK!) and burly enough to cope with rock (the sort of conditions
@Kind of Blue has to deal with but not very common on UK campsites
)…
…but those smooth big blocks are NOT actually very good on wet grass (bc unless it’s very soft and muddy they can’t get the grip), or packed snow and ice for that matter which is what we mostly get (despite them being 3PMSF rated bc they’re still better than summer tyres and can cope with soft stuff
)!
Most people running them are frankly doing so simply for show for the swamper look. Fair enough, it does look quite cool!
Frankly though, you will be much better off with All Season (AS) tyres - that are nearly all 3PMSF / M+S (mud & snow) rated - since the grip pattern will cope better with simple wet grass!
AND it will be a better all-round road tyre for the 99% of road driving you will do!
PS I read your post re camping on grass but see your first post does mention “muddy”; if it’s genuinely thick mud then an AT tyre would be useful but really, how much mud and how often?
An AS tyre should cope fine if we’re just talking about wet muddy grass - unless the mud is like this
Your favorite pic of your Transporter
(bearing in mind that ironically those tyres might actually still be AS tyres but on a 4Mo?!)
…
…and maybe just avoid shit campsites with a lot of mud?
The issue of course I suppose is that a lot of basic campsites - the best ones - might not start muddy but can become so eh?
(I have a 4Mo so less worried!
)
