I think that there are the true large 4 x 4's such as the Range Rover and the Toyota Land Cruiser, and these are the all terrain vehicles used in deserts and snow. I had 2 Toyota Land Cruisers in succession at one time when I used to go fishing over muddy fields and wanted to tow a heavy trailer. They had diff lock, high / low ratio and all kinds of controls.
The costs are high now - a set of tyres at about £600 and road tax at £450 or more, plus depreciation at £5-6000 a year in first 5 years or so. My wife now has a Mazda CX -5 , and this automatically "decides" to use 4wd, the Tax is £120 for a 2.2 Diesel Automatic and it can tow 2 tonnes. Not a true "mud plugger" but very good all round. We looked at the Toyota RAV4,and Honda CRC and this had the best engine for the diesel automatic at the time over a year ago. They all work better in ice and snow - but any vehicle becomes a sledge on black ice if you try to descend a steep hill with the brakes hard on!
Good luck with your choice (PS The Honda was the CR-V, not CRC!)I think the Outlander is Mitsubishi? We like the higher driving position on this type of car where the "bum height above road" makes it easier to slide in and out as arthritis creeps up! I am currently off driving until December (DVLA and medical issues)and am glad we have the smaller vehicle as my wife found the Land Cruiser too big. Hope you find what you want.
I've been into off roading in the past as a leisure activity and had several Landrovers. But for over 30 years since, I've held the opinion that for road use, if a 4x4 represents the ultimate 100% in winter road handling, I rate front wheel drive at about 80% and rear wheel drive at about 20%.
So if I lived in the highlands and expected snow every year, I wouldn't bother unless money was no object. Most modern cars also have some sort of traction/stability control which takes the car to over 80% capability on my scale of ability, which then takes you into serious off road capability to justify 4X4 upfront and running costs to outweigh a modern FWD.
Ice is also a different kettle of fish, we have a Honda CRV which is great in snow but I still have vivid and rather unpleasant memories of sliding down a steep hill on sheet ice in a somewhat uncontrolled manner. The 4WD didn't help at all and at that moment the high driving position just seemed unstable. Fortunately no damage done but not to be recomended.
It also depends where you are, in urban areas winter tyres would probably be as good and cheaper to run than a big 4WD but in the country where snowplows can be infrequent visitors something with greater ground clearence and two extra drive wheels is a lot easier to justify.
My brother got a Santa fe and they liked it so much his wife got one as well, they do live out in the wilds of northern Scotland and it's pretty much a necessity there.