My big sister has a full spec 2.0 petrol 4x4 qashqai, bought it new 4 years ago. It's a good car and even on the oem tyres she had no issues in the snow over the past few years. We live in a place that gets lots of snow and has 'hill' in the title..... As you can imagine, there are plenty inclines and her drive is steep too. No problems at all. She has used it with her child and all the crap that she routinely carts about.
It's not the biggest car (Mums CRV dwarfs it) but it's comfortable and capable.
You can do a lot worse than a qashqai in my opinion.