replacing the beemer

The new Mercedes GLC starts just under $40K and is quite a nice car if you don't add too many options. There are three listed on cars.com about $40K. Also, the GLK (pror version of the GLC) has almost a cult following due to its practicality and reliablity. I believe they did the change over this past year so there may even be a couple of new ones on the dealers lots. If not, MB has a very good "Certified" car warrantee.

I have a 2015 Audi SQ5 and have been very impressed. If you don't get the "S" version, I believe you can get a very nice one within your budget. Since the body style is changing (slightly) in a few months, you may be able to get a very good deal on a new Q5 (or on a 2015 or 2016).

Both the Lexus RX and the X3 are crossovers with AWD and similar weight, so the difference may have been the tires? The main difference is that the X3 is a rear biased AWD system and the Lexus is front biased. If you want something lower maintenance than the German brands, you might also consider the Acura RDX. If you want to stay German, I would try the Audi Q5 as it's Quattro system is arguably better than it's rivals in the snow.

If you liked your x3, and I can understand why, why not consider a CPO X3 replacement? That would cover you for any freak major problems. I've had both BMWs and Audis (also VWs). I can't say the Audi was more reliable, just the opposite, actually. I know that Mercedes can have expensive problems, too. As Michael points out so often on this site, if you really want reliabillity, you have to look at Toyota (Lexus) or Honda (Accura). Maybe test drive new high-end Toyotas or Hondas and see if the interiors appeal to you. Then test Lexus and Accura.

Seriously consider buying a set of winter snow tires. On an expensive vehicle, they don't add that much to the cost.
I had an all-wheel drive Audi A4 with inexpensive all-season tires that was awful in snow (Minnesota) until I put good winter tires on it. WOW! Could not believe the difference. Same thing with a front-wheel drive Honda.

As a couple of others have said, the problem with your Lexus was probably due to the tires, not the car itself.

Any of the Germans can have expensive problems, but the Japanese competitors don't drive as well. I don't care for how the Acura RDX drives, but the MDX handles well. Too large?

Best handling of all: the Porsche Macan and new Jaguar F-PACE. A Jaguar in its first model year probably isn't wise. The 2015 Macan had a high repair frequency initially, but has been improving. None of the 18 owners of the 2016 in our survey has reported a repair yet. But these won't be in your price range yet.

X2 on the CPO BWM. Very good deals on late model X3's with 6yr/100k CPO warranty. 2014's have great reliability (limited warranty unless very late ISD) and 2015-2016's should have good reliability as well. Just a thought. We tried them all. MB 4 cyl is whiny and underpowered (need the diesel, don't hold your breath). Lexus rides.....well, like a Lexus (if you like that sort of thing) and steers just like tuning the radio; smoothly but with no feel at all. The Honda/Acura products seem to have the same interiors that grace the cheapest model in the lineup (not that great IMHO). It's a tough nitch to find a truly 'sweet' car with performance, reliability, gas MPG and a reasonable cost. Nothing will compete with the X3 at the price point CPO. If you do elect to go BMW again, consider dropping the Runflat tires and very carefully watch your tire pressure and tire wear. Two very important factors in keeping the transfer case happy are matching tire diameter (all the way around) by keeping the tires evenly rotated and evenly inflated to Mfg. reccomended (not the same front/back for many BMW's).

cheers.

Stick with BMW xdrive as it is one of few suvs that offer twin clutches to allow power to one single wheel when the others are spinning. The MDX has it but Lexus RX only sends 50% of it's to the rear wheels as oes the Acura RDX and NX200t, both of which fail the incline roller test and actually fall backwards. The RDX system is so bad it had to pushed off a set of flat rollers during a test. The Jaguar Fpace system is a little better and can send 100% forward or back but not left or right. It's torque vectoring brakes the inside wheel on a turn where the most sophisticated AWD system with twin clutches instead sends power to the outside wheel.

The Buick Envision Premium with Twin Clutch AWD offers power to a single wheel and power to the outside during torque vectoring.