A “taller” side wall should have a higher load index. (Look at the side wall on G rated tires). Low profile tires are typically “bling” tires with lower load index.
Wider tires wil float on snow and not bite through. Most of us don’t have a full quiver of tires and the ability to swap tires for different snow conditions. Here in the north east, a narrow footprint, snow flake rated tires is a good choice for winter.
You didn’t really say -above- if you were carrying your TC or not, but running at 50 psi is dangerously low. I wouldn’t if loaded up.
When the TC is off I do air down.
Be safe.