I´m not sure about the standard options in the US, but a 5series should have DSC - helps a lot in winter, with decent winter tyres, you shouldn´t have much of a problem. I even used a 3 series convertible to travel in winter through austria / alps, lots of snow and ice, but nothing it could not cope with ... Just don´t ever try to fit cheap chinese winter tyres on this car....
Check the front track control arms, with this mileage, they are probably worn-out . and test all the electronics gadgets, if some of them are defective, it´s probably going to get expensive... is the automatic air conditioning working fine, especially the amount of air coming out of the air outlets, steady or not... another bmw problem is the blower output electronic system...
with the 2001 series, you´re getting the m54 engine generation, no problems with reliability, they usually last forever, only the vanos sooner or later needs a service / adjustment....
Thanks for the tips, I'll check w/the mechanic tomorrow. The car does have DSC, I noticed the switch during the test drive. I'll thoroughly check all of the random gadgets tomorrow also.