First, here is a tire calculator that I use a lot: https://www.tacomaworld.com/tirecalc
Max tire diameter without a lift 31 inches (maybe 31.5, can't really remember, but 31's will fit)

Second, for a wider stance, you can change your rims to zero offset. This will push your tires out more than OEM wheels. You can google offset and back spacing if you are unclear on the subject.

Now I will address the snow.

Really, it all comes down to math. Only a small portion of your tire contacts the ground at given time. We will use simple numbers. We will use a vehicle weight of 4000 pound (nice even number) and a wheel width of 8 inches with 4 inches of the wheel (front to back) actually in contact with the road at any given time. This means that 32 square inches, per tire, or 128 total square inches of tire are in contact with the road at any given time. What this means is, for every square inch of tire that is actually in contact with the road, there is only 31.25 pound of weight for every square inch of rubber holding your vehicle in place.

Say you go to a 10.5 inch wide tire, using the same example numbers, just a slightly wider tire. 10.5 wide x 4 inches long = 42 square inches per tire, or a total of 168 total square inches (4 tires). This means that 23.8 pound of weight are support for each square inch of rubber actually in contact with the road.

If you are on rocks, dirt, mud, slop, and the like, then you want a wide tire to help you "float" across the terrain without sinking. This can be true of snow, especially in deep powder that has yet to be driven on. However, when you are driving on plowed roads, that usually have a thin layer of ice over the top, or has been packed down tight, you want as much weight per square inch as possible for maximum traction. The last thing want is to float across ice. (FYI, is because of this monster trucks actually float in water, their tires are that wide)

This is why Forest Service trucks in Colorado all have very tall, very narrow tires. I really miss Colorado and need to move back there. I digress ... sighhh ...

The thing about snow is that it is never just snow. There is ice, black ice, hard pack snow, powder, wet snow vs dry snow, the list endless. However, for the majority of driving durring the winter, on roads that are maintained, a narrow tire is better than a wide one.