Does spinning wheels in snow damage the automatic transmission?

You will sometimes get a burning smell with any difficult maneuver. Not a problem unless it is a problem. You never know what caused the smell. Your luck should be good.

as long as the motor didnt strain youll be fine its when your on black top or a hard surface that hurts the motor and tranny because of friction and gear jamming youll be fime

Subaru’s have so many different AWD’s. I have a manual transmission Subaru WRX with LSD on the rear only. When it does spin tires the front wheel goes side to side in a relatively quick motion. There are no electronics controlling this on my car, simply fluid shear sending power. I think the concept is if one wheel spins faster than the other the fluid shears and power goes to where it spins slower(assumes traction).

The rear wheels pretty much both spin which I am guessing is the LSD.