I've seen a few of these videos and what I'm saying isn't meant as a negative.
It's all good and well showing a comparison like this, but not many people will be swapping NEW summer/all season tyres for, in most cases, new winters.
In mine and my sisters case. Our tyres were pretty well worn. Mine were down to about 2mm on all 4 corners and the rears on my sisters were right down, possibly, below the tread indicators. I changed my tyres in November, so before the real cold set in, and the difference even then in cornering and braking was significant.
I reckon, from a legal standpoint, I could've gotten through at least most the winter with the tyres I had on before, but I daren't think how compromised the car would've been. In my case, the winters I bought were about £15 a corner cheaper than replacing like for like with the Pirelli Scorpion STR's (which admittedly were more than fine in previous winters) I had on, so it was at least worth giving them a shot.
Even if I decide to swap them come spring summer, they don't wear down when they're off the car so could easily last two or more winters beyond this one.