Discovery 2 broken half shaft

It's a snowy winter here, the snow it's up to 6 feet high.
I was helping a van to get out of snow, I was in low, a lot of rpm as the van was heavy... and clonk! No drive at all.... Lucky me, engaged the CDL, and drive home like a crippled dog, with only rear wheel drive( a bloody P38 RR was hooted me to clear his way); the oil was leaking out of my front axle, can't see where from exactly.

My questions, is it a sign of broken half shaft? I mean oil leak and no drive...
Trying today to move the car, only the rear left wheel was moving front and reverse, the rear right moves only a little , a few inches front a few inches back. Can be said that front left (or passenger's side...) half shaft is broken?
I just want to know before ordering a new one; OK, I know that it must be checked and wheels turned in a proper space but I want to save some time to order parts.

Many thanks for any help!

you will have to be clearer on your description of whats happening now ,you know its front axle but could be diff as oil leak ,or cv,etc

Now, the car is driving only if the CDL is locked; improper said driving,only rear left wheel is moving,both front and reverse, none of the front, and rear right is just moving very little, a few inches. I can see which wheel is moving as the car is blocked in snow, only wheels are moving...
As the wheels are diagonally linked, I think that rear-left and front right are OK, rear-right and front-left are wrong. If one of the rear shafts was broken, it was no movement at all on the rear wheels isn't it?

how are the wheels diagonally linked ? if front has lost drive to one or both wheels ,you would need cdl to stop all drive been lost through front and give drive to rear,which you had ,if one rear wheel spins in snow there will be no or little drive to other rear wheel ,until you check front axle you cant say what item has failed

Anybody experienced a broken half shaft? I am ready to order a front axle just to be on the safe side but don't know if it's the symptom of a half shaft or front diff.
Is the oil leak common on broken half shafts on Discovery 2? I am thinking that the rest of the shaft is not centered if broken and is pressing the axle seal and the oil is leaking.

Finally, the problem was solved! It was the differential, the front one. About 30k miles ago, when I first changed the oil in it, I remember that the oil was very dirty, with a lot of iron "dust" in it, unlike the rear one, where the oil was clear. Finally, the pin carving an oval shape in the differential body, about double as the pin diameter. The pin was finally broken, the gears broken as well,the diff body brakes, and the rest of the pin punched the differential pan, cracking it.
The half shafts are OK, the second hand diff is perfect (thank you ebay UK), the fitting was very easy (if you ever have to change the diff, you don't have to on-bolt the half shaft from the hub and bearing, the 490 Nm job, just the 4 bolts of the bearing and it comes out). A little welding to the pan and now everything is perfect.
A new 4 pin differential is the solution to avoid that for the future.