I had a 2002 Jeep Grand Cherokee with Quadradrive II (pretty kick ass AWD with LSD's front and rear). I outfitted it with Michellin AT tires year round (it was my winter beater/dirty work car).
The car did very well on deep snow and you could feel the AWD working its ass off to get me through - and it did, but having had many cars with quality winter tires, it just isn't the same. The tire treads helped with deep snow, but they were not nearly as good on plain old slippery roads (ice, packed snow, etc).
You can certainly get by without winter tires. You probably will never get stuck either. But winter tires give you that extra grip that makes a lot of situations totally drama-free.
It also depends on your situation. Do you have the room for the extra set of wheels+tires (or what to deal with swapping tires twice a year)? Is it a 2-year lease or are you planning on keeping the LR4 for years? Etc.