I can say with close to 100% confidence that it there's nothing wrong with the cat, regardless what the mechanic says.

I suspect the code has to do with a lean condition or something related to the O2 sensors. The cause is (likely...) neither the cat nor the O2 sensors.

It is likely the rubber intake boot that cracked at the branch going the idle control valve. If once that is fixed the code persist the cause is the crankcase ventilation system. Before touching the cats or the O2 sensor address these two: they both crap out around the 80K miles. If before checking/fixing these the mechanic insist on the cat, walk away from the car because is time bomb... Really...

When we bought ours I had to get it smogged to have it transfered. I took it to the smog station and the CEL came up: luckily this is our 4th BMW with an M5x motors so I knew what was wrong and I was right. In the process I removed the vacuum line that goes to the flap in the exhaust (now it's always open) and plugged the hole in the manifold. I just wanted to avoid having to go back at a later time because another rubber hose cracked causing a vacuum leak.

Other things that commonly fail on these cars:

1) waterpump and/or thermostat and/or expansion reservoir
- the waterpump has a plastic impeller and a cheapo bearing ($150 for the EMP Stewart WP)
- the thermostat leaks right where the electrical connector is ($60)
- the reservoir cracks right above the return hose form the cockpit ($80)

2) oil leak comes from either the valve cover gasket or the gasket between the oil filter housing and the engine block ($50 for the gasket kits))

3) the transfer case oil IS NOT lifetime. The control module of the transfer case monitors the oil wear and stores a code when it needs replacement. Unfortunately such code does not cause a light to go off in the dash and can only be pulled using the BMW GT1 software. I would suggest replacing the transfer case fluid. (IIRC the oil last ~70-100K mile of regular use). People have neglected this and ended up with a failed transfer case. ($50 for BMW transfer case fluid)

4) windows and moonroof are assembled with little to no lubrication. They have nylon guides that are ok, but eventually seize or get stuck. It's somewhat labor intensive but with some basic tools you can spend a Saturday removing the door panels and lubricating them. Same thing for the moonroof: otherwise it gets stuck (when we bought ours, the moonroof was getting stuck and the windows were very slow). Doing it yourself will allow you to take some extra time to assemble the door cards correctly and avoid annoying water leaks. (lubes, 3M weatherstrip adhesive, duck tape)

5) the doors squeak when going over imperfection: some Gummi Pflege around the gaskets and the felt area of the seals goes a long way ($15 on Amazon)

6) There was a recall for Bremi spark plug coils, but Bosh can be just as bad. If you get misfires on a specific cyclinder mote the coil around and see if the code changes along with the coil. If so replace the coil (~$35)

7) Don't be surprised if you go through 1 qt of oil every 3K -5K miles: that's just how the M54 is...

8) The battery compartment is made of metal and prone to corrosion if the battery leaks. In my case (and this is the second BMW that I observe this, the other was a Z3) the previous owner replaced the BMW with an aftermarket batter which fit quite about the same but not all the way. It wasn't secured right and acid spilled. I caught it on time and got it resolved with some baking soda, warm water and some spray paint. But do yourself a favor: if the battery goes kaput, get a BMW batter. They cost a bit more but they have lasted me an average of 7 years. Let alone, they won't move around, or start leaking.

9) You might occasionally get a "Check Fuel Cap" light after fill up. There was a TSB on the subject which was resolved with a ECU software update (the ECU monitors for fuel tank leaks by basically pressurizing it and measuring how much the pressure drops - the software update likely lowers the threshold that triggers the light). In my case I was able to resolve it by removing the green seal from the fuel cap and coat it with some silicon lube.

As far as snow performance, since I live in CA I don't buy snow tires, but use chains when up the mountains. Last month at Big Bear I pulled an H3 out of a ditch. The X3 had two chains on the rear and there was about 1 foot of snow on the road... Your result may vary, but for me the X3 works just fine in the snow. In the summer I use it to haul the toys to the track: 3 people and 2 motorcycles plus gears and it didn't have any problem.