I have no doubt whatsoever that the improved wet handling of a winter tyre is partially attributed to tread depth - they intentionally have 10mm of tread for a reason. But they will wear, for sure. At some point, they will have 6mm of tread, which could be the same as a summer tyre.
Even with the same tread depth, however, the actual pattern of the tread will give the winter tyre better wet cornering, better wet braking and reduced risk of aquaplaning - even on a warm day.
On a cold day (below 7C) the rubber on a summer tyre freezes and goes hard. This makes it more brittle and more prone to slippage - this creates increased wear on the tyre, reducing its value.
Where you live has absolutely no relevance here - being on the correct tyre reduces wear, full stop.
There is no increased overall cost with winter tyres and you can actually end up saving money.
If you fit a set of summer tyres to your car, they won't wear at a fixed rate - they will wear more in the colder months. If you take them over during this period, replacing with a more suitable winter tyre, you eliminate this high wear period and save the summer tyres for the warmer months in which they operate best.
Ultimately, if the tyres cost the same, you are better off wearing 2mm off a winter tyre than you are by taking 3mm off your summer tyre in the same period - and you end up safer on the roads on cold/wet days. It doesn't matter about driving standards, or driving to the conditions, a winter tyre will ALWAYS stop quicker than a summer tyre in the cold/wet. If a child runs out in the road from a blind spot, or similar, you have more chance of stopping when using the winter tyre in the winter months. This is, by definition, safer.
In my eyes, it's a complete no brainer. It's safer and overall cost is the same.