I probably have several hundred US dollars worth of running stuff on hand at any time. Sure, I could just throw on an old pair of shoes, but I'd freeze or injure myself right quick and that would end up being even more expensive. Running once in good conditions is cheap. Running continuously in all kinds of conditions is less so.
That sounds right for water, but definitely not true for snow. I don't run when it's deep on the ground, but even a little can splash onto the uppers and then soak through. It's like running through shallow puddles half the time, not fording a stream. I know from experience - maybe a thousand miles of running in New England winters over the last few years - that Gore Tex and similar barrier fabrics avoid that problem quite well.
Those same shoes usually come with high-traction soles (both materials and tread pattern) which are also essential in those conditions. And of course they're warmer. Winter running in summer shoes would be a recipe for freezing, blisters, or injury around here.
After a few years as I had more experience, ran faster (and warmer), these issues mostly disappeared. Nowadays on winter I only run with shorts, a thin hard-shell, and thin shoes (sometimes five-fingers) with temps of -5C. Some days get much colder (e.g. -10 or -15 C) but when I've used some of the warm clothes I used in the first couple of years of running they've always felt too warm. The only thing that's still an issue is running in the dark. Independently of whether I know the trail, have a head-lamp, etc. I run slower in the dark than during the day, except on the track. So now when its dark, I always go to a running track to run. Most of them have lights on till late, and some schools, most universities, etc. have one and they let you use it for free.
I guess it would be nice if I could run wearing less, but I honestly don't think it would be safe for me. Your mileage obviously does vary. ;) As it is, I have winter shirts, undershirts, and socks that are all different brands, and I am keenly aware of which ones are better at which temperatures. There's a bit of an art to wearing exactly the right level of gear for the conditions, and I've simply had to become good at it.
1° it's more than 12-15°C outside : shorts and short sleeves
2° it's less than 12-15°C : long tights and long sleeves
3° it's less than 5°C : add cap, gloves and microfibre top to the previous set.
4° it's raining: I'm not made of sugar :)
5° it's heavily raining : I wear a cheap rain poncho, it's fine.
All my sport wear is the cheapest stuff from Decathlon, 5 euros shirts, etc. The rest of my gear probably cost me less than 150 euros and I've been using all the same gear (but socks and shorts) for 10 years, it doesn't wear out much.
I wear the exact same socks and shoes and short-sleeved running t-shirt whatever the weather is. I only use one sort of anti-friction stuff: 3M tegaderm. Exactly 1 square cm2 of it on each breast. A roll lasts a couple of years or so. I threw away a pair of shorts that hurt me at the thighs. I don't carry any money or phone or anything but my home key, in the small pocket all shorts and tights have. I don't carry water either, because I don't run more than 2 hours straight anyway, I drink before and after and that's fine.
I had a couple of injuries after turning 45 but it's nothing gear-related, really.
Above 5C: normal/light gear
0 to 5C: add light beanie and gloves
-5 to 5C: add long-sleeved shirt (over compression T) and tights
-10 to -5C: jacket instead of shirt, warmer gloves
-15 to -10C: balaclava-style mask instead of beanie
Below -15C: just don't
I'll often go "down" a level if it's windy and/or moist, "up" half a level if it's an unusually short/fast run. The main thing is that as long as I wear the right gear I actually prefer winter running. It's quiet, it's scenic, and I have control over my heat level. What I really hate is the hot humid days of summer, which I can't do anything about.