A cheap tire, summer or winter, will be fine almost all of the time. They will do most of what you ask them to sufficiently. But, when shit hits the fan and you need to start/stop/maneuver quickly, you may end up pushing the tire past its capabilities. I value my personal safety and my family, so I buy tires that will give me the best odds of coming through in crunch time. Some folks don't have the $ for better tires, or they play the odds with cheap tires (and are very likely to be totally fine).
My grandpa lived hard and didn't give two shits about anything: smoked like a chimney, drank like a fish, no exercise, worked too much, and he lived to 75...odds be damned. Just like the guy that runs bald summer tires through every winter and comes out unscathed. But I'm a numbers guy, and I'll do what I can to stay around for as long as I can
