Yes, your SJ can handle these conditions and much more besides ( I like to look at my LWB SJ413 as a Land Rover Recovery Vehicle !! ), but the little car will need some other equipment before you go taking it to the rough. The first thing, the most important thing in my book, has got to be tyres. You will not get far on standard road tyres. A good set of mud tyres are reasonably cheap and will transform your SJ. If you do not like the noise of these knobbly tyres while driving on road a good simple way round this would be to invest in a second set of wheels, one for your road use tyres, and one for your play day tyres.

It is also worth taking recovery equipment. A Hi-lift jack is a great investment, as is a basic hand winch, tree straps and good winching gloves. Another few useful items are a spade, an axe and a saw. Useful extras would also be a set of traction ladders and good strong rope.
Depending on where you are greenlaning, you could be several miles from anywhere so it is also a good idea to take with you a small camping cooker, a kettle with beverages, a full fuel can, a spares kit (containing - fuses, bulbs, fan belt, etc), a can of Tyre weld, a fire extinguisher, a mobile phone (it is worth remembering that in a high percentage of the greenlanes of Britain your mobile phone will not have a signal), and if possible, a First Aid kit and training.

It is always better if you have someone to go with you and even better if they have a vehicle, as this will help recover you should you get stuck. Remember, if travelling in a convoy, to always ensure that you keep at least one other vehicle in sight. Never start to go through an obstacle such as a large descent, until you are 100% certain that the vehicle in front of you has cleared the obstacle and so your path is clear - you could lose control and slide down into the other vehicle leaving you all in a mess.

Driving through fords - great fun - but do so at a sensible speed. The SJ is very good at wading through water but not invincible. Take it easy and you should create a bow wave in front of you that will make your crossing easier and safer.