Okay there's a lot here. I guess I'll start with the raincoat thing. I've got two that are perfectly comfortable to wear in the summer. They are incredibly lightweight and can be unzipped for more airflow. In winter the key is to wear a jumper underneath.
What I'm trying to show you isn't that the weather doesn't exist, it's that it doesn't matter. The city I live in I don't have to spend more than 5 mins under sunlight or rain for each hour of commuting. The sidewalks are covered, and the tram stations have shelters. The only time I'll be in direct sunlight or rain is while I'm having to cross a road. This is a direct way in which city design alters the impact the weather has on me. Not by changing the weather but by shielding people from it.
Another thing is that car dependent infrastructure, such as roads and parking lots, are massive heat sinks that absorb massive amounts of solar energy and continuously radiate it as thermal energy. In this way car dependent city design actually does change the weather and make cities hotter.
Going back to the city I live in, all of my commutes are sub 30 minutes. Dentist, hospital, work, university, general store, hardware store; you name it, I can get there. This means that any weather related impacts are severely reduced by merit of not actually being outside all that often. Even during a 30min commute that will be time spent in an enclosed air conditioned space such as a tram or train. Using the ratio from earlier I'm realistically only gonna have to put up with 150 seconds of rain on the worst of days. This is because of the way my city is designed, it directly affects my weather exposure.
The statistical analysis I'm referring to is looking at a city with bad weather such as Oslo which the video referred to. Confirming for yourself what the weather is like there, cold and often snowy. And then checking with commuter statistics to see that yes despite the conditions, it doesn't stop people from commuting on public transport, bicycle or just their feet.
I'm not lying to you. I'm not trying to deceive you. I'm just saying that as someone who lives in a walkable city, I don't get rained on and I don't sweat my balls off. This stands in direct contrast to what you've said your experience is. I'm trying to show you that the reason for this is because you live in a city that isn't designed to be walkable, while I do. The weather doesn't matter, your city just isn't designed to handle it. This is the fault of car centric urban planning.