Taking the front strut bar off is not going to make a huge difference, but it will make the car a little bit softer as far as body flex and roll. To a driver who doesn't have a lot of experience with aggressive driving, having a softer platform will make the response less "harsh", therefore the suspension may be more to his liking, and feel like it handles better.
But really, if you're driving in the snow, I think any difference in handling is going to be imagined, because the strut bar doesn't even come into play until the chassis is being pushed hard enough to flex.