I use a Pirelli MT43 on my Suzuki DR & my friend also uses one on his Sherco 4.5i. Fantastic tire -- we both love them! I works magically in rocky/rooty terrain & I don't have any issues with it in the mud either. Sometime it grips too much, like if you need to turn around in a tight spot & you want to spin the tire to swing the bike around. I have not tried it in sand but I would image a wider regular knobby might be better?
I have about 1100km on mine (lots of highway) & it still looks great. Bombing around town I run it with 22 psi. On the trail I drop it down to 14 psi but that's because I do not have a rim lock. My friend runs it at 10 psi on his Sherco (w/rim lock) but I have heard of other riders running it as low as 6 psi.
The MT43 is the only DOT trials tire that I know of. The thing is, it's not "exactly" a trials tire. Sure, it may look like a trials tire, but it is in fact different from a true trials tire. The MT43 has much stiffer/thicker side walls than a traditional trails tire, and deeper/harder lugs because it is designed for much longer wear.
Funny enough, I got the idea to run the MT43 from a Husaberg rider I met on a trail last year & all he did was rave about the tire -- he was on a FE650.