At the ski hill we were using the trucks at off hours as a poor employee cat ski operation.

We are obviously talking different environments. When the ground is soft and relatively bottomless then floatation is the key. There is no sense in digging down through the gunk if there is nothing to dig down too. Many vehicles can be "floated" on mere tires.
For example:
Tractors with multiple sets of tires front/rear so they spread their weight more and don't sink in soft fields.
Quads: If width was bad then quads would be running bicycle tire widths. Quads are much better than motorcycles in truly muddy/bog situations.
The big Iceland trucks which traverse the soft glacier snow.
Now on frozen ground with a foot or two of snow/mud/slush (probably your typical northern lolgging road) then yes a nawwor aggressive tire (preferably with chains) will claw down to the hard surface better than a wide tire.