I got curious.
In 285/60R18 on tirerack of the tires offered here are the "winter/snow" ratings 1-10 from customers for each tire
Defender 8.4 (good)
BFG Trail Terrain 8.2 (3-peak)
KO2 8.7 (3-peak)
General Grabber AT 8.7 (3-peak)
Toyo AT3 8.8 (excellent) (3-peak) (I concur with this rating)
Note that number of reviews for each tire vary significantly.
So at least some reviews show one 3-P tire being worse than the non-3-P defender. But those reviews also put other tires performing significantly better than the Defender LTX in winter conditions.
I found it interesting that what tirerack calls the OE tire for us, the bridgestone dueller D684, scores a 4.4 in winter/snow. Ouch.
I think @ace10 is on point about grains of salt. And that any of the tires with positive reviews on a broad scale will serve you well.
That's a pretty good frame of reference. In my experience, the Michelin LTX were significantly better than Cooper AT3 (3pms but still not a very good snow tire) and about on par with KO2.