None of those vehicles are really SUV's (X5, Highlander, etc.). They are cars with a high seating position and some extra ground clearance - unibody construction, fully independent suspension, AWD only (no transfer case/4WD), drivetrain designed for car type rather than truck type usage, etc. Call it a crossover, but it's really just a car.
It's a good comparison to look at a lower slung performance car vs. the taller model. Those tradeoffs are far narrower than against a body on frame SUV with a solid rear axle, low range transfer case, big displacement V8, etc. I think these days you have to define a vehicle by the extent to which it has mechanical vs. electronic design.
If you have a base design that mimics traditional heavy duty mechanical traction (to the extent that is possible) with a car body/suspension then it really is just factors of weight/COG, space, fuel economy, etc. Apples to apples stuff. If you are comparing all of that to mechanical designs (low range gearing, differential locking, etc.) plus heavy cargo capability, then you've got oranges and the range of compromises (and what one may appreciate in terms of performance) has gone way up.
Most folk these days are just eating apples unless there is a specific need otherwise, but that leads to the inevitable questioning of oranges.
I don't think there's any point in arguing semantics. The original question posed was "Why do people choose SUV's for winter travel?" We're talking about the general public and what they're buying. For the most part, the general public doesn't care about your distinction between crossover/SUV (both of which are made up terms anyway, you can define them however you want). The general public also buys a whole lot more unibody "crossover" SUV's than it does body-on-frame SUV's. So those are most relevant to this discussion IMO.