Tires is everything in snow but also snow condition, we had close to 2 feet(yes feet of snow in Seattle Xmas week). After rain for 3 days, I almost got stuck going up hill with snow chain on 1 year old Pirelli tires.
well being 19" wheel with 285 tires didn't help either.

Back into the garage, put the Dunlop performance snow tires set(no stud). It was way better.
In 20 degree cold my Pirelli + chain would be fine up hill not in 1 foot of slush though.

All in all CRV is not better than nX5 (maybe worst ) cause it's not even AWD, it's front wheel drive in normal condition then xfer case put torque into back axle upon slips. X5 is 40/60 front to back in normal condition.
The best would be 4wd with lock diff and off road tires. My neighbor is the first to come and go in 2 feet of snow in his subbie, up and down the hill of our private road.

I'll say go get the snow tires, if buying used just make sure the thread depth still around 9-10 of 32nd inch deep. The best deal was $950 from tire rack but with centering ring on 17" wheels. Not sure if they still have them. S/H was around $120.

Good luck, btw only drive in severe weather when you have to, other drivers may do so without a good set of tires and hit you.