To answer your question.....yes and no. If you have a newer jeep then your front axle is always turning, whether 4wd is engaged or not. A locker in the front will STILL engage even in 2wd. If your jeep has manual locking hubs installed on the front axle, then your front locker would not engage unless you locked your front hubs. Manual locking hubs are not standard equipment, and unless you or the PO installed them, you probably don't have them. So yes, your locker WOULD still engage.
But installing a front auto locker is not a bad idea when used on ice, put a manual locker in the back when the money comes. As I stated earlier, physics dictates that the axle that loses traction wants to lead. If your front axle loses traction because of the locker, then it will want to lead and since it already is....that is a good thing.
A change in acceleration is what causes trouble in icy conditions. Positive acceleration or negative acceleration (braking)is where it starts. The reason a locker CAN be bad on ice is because if both tires start to spin, then traction is lost and the trouble starts. An open diff only drives one wheel. so the theory is that only one tire will lose traction, as the other isn't "driven". That theory doesn't always hold water, but that is the reason, if you buy a new car with a limited slip differential, it comes with an orange sticker warning you about LSD's on ice.
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