If you are asking about "P" for passenger rated tires, they are, in my opinion, unsuited for any type of extended off highway use. The sidewall and tread are both much easier to damage or cut.
The sidewall on an LT tire is stiffer, and the tread is usually stiffer, so they will ride more firmly on and off the pavement. To make the ride more comfortable and to gain traction on dirt, rocks, mud, and snow I decrease the air pressure in the tire. My normal tire pressure is 32 PSI, and for general off highway use I drop down to 20 PSI.
In sand, snow, mud, or rock crawling I've gone down to very low pressures to gain both traction and flotation. In those circumstances I've gone as low as 6 PSI. Caution must be excessed at those pressures to avoid unseating the bead of the tire, and you need a source of air to refill the tire prior to driving on pavement or even hard packed dirt at speed.
My primary off highway vehicle is on 32-11.5x15 GoodYear MT/R's, a tire I consider to be the best tire made for the type of conditions I see in the southwest area of the USA. My wifes truck sees less severe use, but still gets out on moderate trails. It rides on 265/75-16 GoodYear Wrangler Silent Armour tires. They are an all terrain type of tire that is much quieter on pavement, yet offer good traction and outstanding toughness. They are made on the same cut resistant tire carcass as the MT/R.
Hope this helps!
Mark