It won't be the diff, as it will be still turning as long as the wheels are rotating.
Not necessarily. If the crown and pinion gear teeth are worn sufficiently, or the lash adjustment is incorrect, they will make a whining sound under load but can be quiet with the foot off the accelerator because the teeth are not under load. The OP says he experiences the whining when not accelerating, but even when cruising with a light throttle, the whine will be present. The test is to see if it disappears when he lifts his foot off the accelerator. I would be looking at the diff gears, oil level and lash adjustment between the crown and pinion first. If they are all ok, it could be tyre noise In my experience, bearings tend to make a rumbling sound which increases in volume as speed increases. I haven't heard a worn bearing whine like Savvy says, but have heard plenty of them rumble.
Drain and replace the oil first off. Check the old oil for colour and any metallic fragments which would indicate the gears and/or bearings are worn. With both rear wheels off the deck, check the backlash at the rear universal coupling to see it isn't excessive. If the tailshaft has more than about five mm of free play back and forth, the lash may need adjusting which is really a job for a diff specialist.
