He is spot on regarding Winter vs Summer tires in the cold weather (even states the normal recommended temperatures of Summer tires right in the manual). I have driven Summer tires in warm rain, and cold rain. I've also driven All-Seasons in warm vs cold rain. All-seasons are NOTICEABLY better for lateral and longitudinal grip (to the point where my wife and I both prefer the All-Seasons over the new Dunlop Summer tires on our BE wheels). When I stress "noticeable", it is practically at almost every turn, and from almost every stop.
Regarding the Winter tires (I haven't had any on in the past 4 years, so I'm not sure if the tires changed), but they are MUCH better in snow for longitudinal grip (if there is such a thing in snow), but lateral grip was similar to the All-Seasons. If you drive in the snow, using Winter tires, the compound never really operates in its desired temp, which then not only turns the Summer tire into a roller skate wheel, but also may deteriorate the rubber (because it has become frozen, and may start to chip away (instead of give)).
For me, in NC, I use All-Seasons all year long, and have no problems with grip (except on ice).
*edit: (None of this applies to those who drive as slow as possible everyday, everywhere - and/or who wished to never have purchased a sports car, regretting not getting the Prius or Smart Car, or is trying to equate anything I've just said to any other car, especially RWD)