" It has brand new Cooper All Weather Tires "
You want real winter tyres, not all weather. All weather really means marginally good for summer and poor for winter. And yes you really need four tyres, not just two. If you have to have only two put the best ones on the back.
Yea, on the back. Winter driving is about driving safe. Gutting stuck is a real bother, but loosing control is a serious danger. You need four good tyres to maintain good control.