You need to check for evidence of gear oil leakage from the rear differential of the vehicle. It sounds like you are low, causing the noise. If it is low, and you have been driving it for a while like this, you may have caused damage to the ring/pinion gears, or possibly the bearings.
The obvious places to find leakage is at the pinion seal, which where the driveshaft is attached to the yoke of the differential. Look on the body of the vehicle for a dark discoloration. Gear oil will rand to get flung in an ark up into the body (and all around for that matter) leaving a gear oil stain. You can also check the bottom of the flange for wetness.
If that doesn't show anything, check the bottom of the differential housing where the rear cover is attached. You may see a drip formed there. Carefully run your fingers there to check for wetness.
If you still aren't seeing any leakage, there will be a plug in the rear cover which should be a little less than half-way up the cover. Take the plug out and verify the level of gear oil on level ground. You should be able to feel the gear oil if you stick your finger in to the first knuckle (about 1/2 inch or a little more than a cm from the whole). If it is low (you don't feel you finger sticking into the gear oil), you'll need to add some gear oil. Get some 75W-90 gear oil (80w-90 will work as well, but you might not find it). It is tough to fill the diff, especially in cold weather.
If the diff is low, you need to find the leak. If it isn't low, you have a major problem with your differential, as it should be quiet. The noise is either made from a a lack of gear oil, something is misaligned due to wear, or both (lack of gear oil causing wear). If getting your rear differential back to a proper oil level doesn't solve the noise, you need to start looking at repair.