"most wide tires period aren't good in snow and ice."
The thought used to be that narrow winter tires would dig down to a firmer surface for more grip. Now the thinking is to use the stock tire size. Here's what Continental says:
"When it comes to the winter season, there are definite advantages to fitting your wheels with wide tires over standard narrow tires.
A wider tire equates to better performance on dry or wet roads and compacted snow. They provide excellent performance in all winter conditions because:
- More sipes interlock with the ground, even on snow;
- Shorter braking distance due to larger tread blocks;
- Consistent and balanced drivability and better steering precision;
https://www.continental-tires.com/car/tire-knowledge/tire-basics/wide-tires
The FWD and AWD owner's manuals I've seen always say to put chains on the front tires of FWD-oriented vehicles. That might be because of the FWD nature of AWD drivetrains in those vehicles. My current CX-9 AWD is included in that list. I agree, chains on the back keep the back in back when braking, especially on a downgrade. If I was driving, say, down from Powder Mountain when the road was really slick, yep, chains on the back in that instance. That road might be steep, but it's narrow.