Actually LACK of tread can be better for stopping distance on dry surfaces. Racing cars don’t use treaded tires on dry pavement, they use slicks because it isn’t the tread that drips dry pavement, it is the softness of the rubber and the surface area.
In wet conditions the channeling of water is not as important in braking as it is in cornering. So better tread to the rear is still the right plan.
Your best bet would be a nice new set of actual winter tires (not all season tires). FWD or AWD, they make a big difference, especially in steering and stopping.
We’ve argued about this for years and I always preferred the best tires on the drive wheels. I’ve just given up though and get four tires now. I just had four installed today and free rotation every 6000 miles.