I mow mine at the same height (higher than you mow) unless I'm scalping to prep for overseeding. If you have problems with snow mold, it can be a good idea to mow lower for winter, but otherwise, I don't think it's needed.

Cutting off more of the grass blade at any time limits the grasses ability to use sunlight to manufacture nutrients that feed the plants roots, it is never a good idea to mow lower.

Depends, if the grass is laying over or if lowering 1/8 to 1/4 does not cut into the brown or stress the grass lowering the blade can be beneficial during the winter as this helps to combat snow induced fungus and helps maintain a higher soil temp which will help with root growth and microbial activity. This will help with plant uptake of nutrients. That said if the turf is very thick and will be stressed by lowering , I would leave at 2.5 and lower to 2.25 for a early spring cut before raising the mower back up . BTW my last cut last season was 2.25 and my root depth measured in the spring was 8+", so IMO mowing seasonably shorter will not hurt root depth as some will suggest.