I have owned my AWD '06 RX400h since early 2005 (2nd one to hit the road in my state). Being that this is Minnesota and we get to experience every kind of weather imaginable, I can honestly say I have never gotten it stuck. I've also never experienced the AWD lock out problem.
IMO driving on snow and ice has more to do with tire design and tread depth than the vehicle itself. That's where you'll need to be very careful. If you read the forums, you'll see a lot of grumping regarding tire lifetime on the earlier RX's. I'm on my 3rd set of tires and don't have 80K miles total on it. I drive it every day but I live ~5 miles from work. It's the age old performance and ride comfort vs. wear and noise problem. You can buy tires that will last longer but bthen it rides and sounds like a pickup. If buying a used RX, check the tire tread. If there's 4-5 32nd's left, you'll probably be paying for a new set within a year.
My batteries are still seeming to be going strong so I can't offer any more insight than the other members on this question.
Being I have an '06, I was affected by the inverter recall problem. Completely covered under warranty. Other than the inconvenience to take it to the deal (75miles drive one-way), it was completely replaced a little over a year ago and all has been fine since. I didn't have any catastrophic failure while driving.
All in all I'm quite happy with the vehicle. Along with a recall or two everything has been covered under warranty. The only other thing is I've had a couple little annoyances with the Mark Levinson audio system. The worst was it ate a CD once and the head unit had to be pulled to get it back. The dreaded "Error 04".
The internet is your friend on this one. I did not take it to the dealer and pay several hundred bucks for them to pull the unit and potentially have to send it in to be disassembled. Only had to buy a magnetic socket and I was able to pull the head unit myself watching the youtube video. Once removed, the trick is to leave the unit plugged in, turn it upside down, and then hit the eject button. The disc cassette get's hung up and won't move slot 6 all the way up. Gravity fixes that problem. I supposed it would work to use a hydraulic turn table and invert the whole car -- but that seemed a little excessive. 8*)
Good luck on your search.