The tread passed me by.
It is a personal preference, but I would not drive through Winter (snow) with 4 season tires on any car. Especially with the Insight as I put more air pressure than a normal car and this leaves less contact to the ground.
I have never had problems with the under body plastic covers but some did. I suppose that I was lucky but I can assure anyone that if something can happen, it always happen to me ( I got rust, corrosion, on a door in 2001)
For potholes, I think that having more PSI in the tire than normal cars and having a lighter car is beneficial to the Insight. Less chance of breaking. But again, some have had problems here as we have Many of those here (salt, above freezing in the day, below freezing in the night). But I had lifted the rear by an inch for better comfort. And this could make a large difference in the pothole season.
Remember that the suspension is really soft and that if you think is is hard, it is because the suspension travel was not enough. It bottomed out.
As with any car, try to avoid potholes.