Actually the contact patch DOES affect the traction, a great deal. Otherwise racing slicks would be no more effective than bicycle tires.... think about it
'Splain how the size of the contact patch has nothing to do with it......
I grew up in the Ozarks. While we didn't have a lot of snow, we had some of the WORST conditions to drive in. Hills, curvy roads, and a climate that would often cycle between being above freezing during the day, and below freezing at night. Can you say ice? At least one bad ice storm a year.
It's actually easier to drive when it's frozen all the time, trust me.
Anyway - there are theoretical nuances, and then there's the real world. All explained by physics, but there are some factors that are simply of no practical matter. Tread compound, for example, means VASTLY more than where the drive axle is. Learned that once when I bought some GREAT rain tires in the Florida summer.... an inch of the first snowfall of the year back at college, and it was like driving on skis....
Barely made it to the tire store on roads that had the tiniest incline, to get some reasonable tires for the weather.
I've had plenty of FWD and RWD vehicles in snow/ice, and once in a while, mud.