There are 4 main essential things for taking a vehicle off road...
Driver
Tyres
Ground Clearance
Grunt.
If you look at all the professional off road vehicles, like the Electricity board, telephone companies, search and rescue, army... They all have good driver training, AT tyres, maybe extra ground clearance, and tend to have larger diesel engines.
As far as driving goes, you need to know how not to get stuck in mud, and that applies to any car you drive, Things like, picking your route, not allowing the wheels to spin in the first place by using the right gear, often 4Low is out of the question in Mud and Snow, and in fact, most times, so is first high. Half the people who off road take their cars into the most ridiculous places to try and prove a point, and then when they get stuck, enjoy the challenge of getting back out again using their toys, in the real world, if you had to off road to get somewhere, you would have driven round it, and gone out of your way to try and not get stuck.
For tyres, you need tread, bald, or barely legal road tyres are not going to be good anywhere other than bone dry hard stuff. But even reasonable tread road tyres, with the pressure reduced will work wonders in light mud. If you want to hit the real mud, you need the benefit of good tyres, designed to work in mud, which includes having tread patterns that go out onto the wall of the tyre, to allow you to use the edges to get grip as well as the bottom, and again, need to reduce the tyre pressure, so they can do their job properly.
Ground clearance is important, as the more of the vehicle that is off the ground, the less chance of getting stuck, so picking a sensible route is the important thing there. The main problem is, Landy's are pretty cheap and easy to mod, so you very rarely see a bulk standard one, and as there are more of them at P&P days, they tend to make the ruts deeper and deeper, and therefore harder for any "Standard road going" 4x4 to be able to go through the ruts keeping the body off of the centre. Unfortunately, the only way round that problem is to lift your own car, or try and run out of the ruts.
Grunt, this is a hard one, you need power to the wheels, to climb and pull, but often it is not so much about how much power, but how easy it is to control. The best way not to get stuck, is to never let the wheels spin, and that is done by keeping the power under the slip point. The more wheels you can drive, the better, so having a LSD on the back, helps keep the drive even, and since there is no centre diff on our toys, you then have the advantage of still having drive at the front wheels, but with them, which ever one has the least traction will get the drive, you just have to hope the back wheels are doing their job, to keep the fronts hard on the ground.
I have taken my "road legal", touring tug off road, and even with all it's road going creature comforts, and additions, on road tyres, she went everywhere I wanted to go that was within her limits, there was no point in taking her into the mud pit, as even fully togged cars were winching out, and on the occasion I saw Rick, his heavily modified Terrano was getting in and out of places heavily modified Disco's and Landy's were getting stuck. There was one hill both me and the wife were playing on, going up and down, that was loose dirt and nice and steep, but with a nice run out at the bottom. A proper trials bob tail came over to go up it, and was getting stuck only 2/3rds the way up, wheels and dirt going in all directions, engine rouring, the car bouncing all over the place, and at one point starting to twist sideways, and risk rolling. He eventually got up, after 4 odd attempts, and a lot of speed/momentum. We drove up it again, after him, no peddles in first low...
Personally, I tend to think that if you drive a landy, you either don't care about it that much, as they are "two a penny", and you just use speed and momentum to get you every where, or you have to drive it so carefully so as not to brake half shafts etc, you drive it properly, and can take it almost anywhere, like any other well driven off-roader.
I would say, take your own to a P&P day, and have a play, start out easy, and get a feel for her, then try a bit more, if everything is working as it should on your car, you will be amazed just where it will go, and to be honest, most times, I run out of bravado, before the car runs out of ability.