Thank you, your kind words are appreciated.

Let's discuss Rims and Tire Size first...
Tires perform best, when the Rim and Tire Tread Width are the same.
This permits the Sidewalls to run Vertically, which makes several positive contributions to the Tire's performance. If you intend to forgo new Rims at this time, take time to measure the Width of the Rims you have on now, and buy a Tire which accommodates that Width.
One can alter the size/outer diameter of a Tire as long as all 4 are the same. Depending on what Year or Drive (2/4WD) you purchase, most newer vehicles will have an ABS Brake system (imho: the best thing to ever happen to vehicles).
The extent of that increase, will be regulated by how much room you have in the wheel wells of a specific vehicle. The information about what original size was intended to be used, is located on a sticker/placard on the drivers Door. The diameter of that size, is what the vehicle was originally intended to run, and would operate the be best with. An increase in that diameter, poses slight to major effects in the handling and performance of the vehicle. Don't be surprised if the size tire being used and what is says on the Placard are different on a used Vehicle.

Now about the type tires...
Your re-definition of requirements makes the Tread you originally selected a bit more applicable. However emphasis on Snow and Mud imply a Tread with a more 'Cleated" pattern. Those Cleats when properly set enhance Wet Traction as well. One thing that Cleats aren't is "quiet", so, you have one or the other... ie: good performance under those (snow/mud) conditions, by giving up a very quiet ride and a longer life Tire.


There are other Patterns which are more dedicated to Snow/Mud (which add up to the most use you expect to encounter). Would you like to select another Pattern for discussion ?