What about checking out Subaru Legacy or Outback or Forester, probably more reliable than either of the current contenders. It sounds like you need traction rather than off road ability, so I would be looking more at 4 wheel drive cars/estates rather than an outright off roader like a Discovery. All that extra weight, bulk and inferior dynamics for no real purpose.

Op is referring to Discovery Sport (Freelander 3) not the Discovery itself.

Tyre choice will be more important than car brand in the conditions described - I'd use All-Seasons for 8 months and then full Winters for 4.

Winter tyres in winter on either would seem to be the way forward. The OP was asking about Disco Sport or X3, I'm sure they've given due consideration to their choice and discounted various Subarus so why bother suggesting something they're not considering (with good reason). Personally I'd go for X3, I'm not generally a fan of German cars but in this case the horrendous aesthetics of the Disco from the back would make my decision for me - anyone else think the rear track is too narrow for the body?

The Disco Sport beats the latest X3 and new Merc GLC in all the tests, now it has the new Ingenium engine it seems the best by some margin. If you don't do any off roading, fiellds, bad lanes then the X3 for normal driving may be well suited and a set of winter tyres for the cold snap should give you all the 4wd performance you need.