Not necessarily.
Your Mustang probably has wider "performance" tires while your minivan has narrower all-season tires.
Somewhat wider, yes, but the same BF Goodrich All Season Radials. :-)
When there is so much snow that even narrow tires don't reach the pavement, or the pavement underneath is ice, the wider tires should actually do better.
Your Mustang has lots more torque than your MV.
Very true, but I know better than to torque the tires in the snow. I tend to start off in second gear during the winter.
And, your Mustang has little weight on the driving tires while the MV has lots.
Which is a function of RWD vs. FWD.
If your Mustang is a manual transmission car and while your MV is an automatic, that makes a difference too.
Yes, the manual should be easier to drive in the snow due to the greater control over the application of power.