We had a Hyundai Tucson which we sold early this year when we decided to stop touring. I used it for fishing which enabled me to drive down a few stee p slopes to car parks and a lane/bridleway which is a struggle in wet weather. Would the likes of a Nissan Quashqi with ESP and high ride height be better than my Nissan Note?
On my wife's old car the ESP was more of a hindrance in slippery conditions, she could not get up our lane in the snow and ice with it switched on. Turn it off and allow the wheels to spin a bit and she could.
Why not get any car with reasonable ground clearance and fit it with decent all terrain tyres?
A couple of years back, I had a 4wd version of the Quashqai as a courtesy car for a day whilst my Nissan Patrol was in for service. It worked very well on packed snow with no drama at all.
To answer your question, no, I doubt it would be any better than your Note, in fact as it is heavier it might be worse. In slippery conditions a small front wheel drive car will be better than a big one. A 2wd car that looks like a 4x4 will be no better than one that dosen't. You could improve grip on your Note by fitting winter tyres.