Why yes, yes you do!
While this is hardly a scientific test, it does illustrate the point well.
The tester has winter tyres on the heaviest of the three 4x4 vehicles which makes it up the drive with comparative ease. While the Range Rover sport is no light-weight, it does have the most capable four wheel drive system, yes still struggles from the outset on it's summer tyres.
Conclusion? On snow and ice four wheel drive is no substitute for the right tyres.