As a pilot who has had 18 months' experience of flying the 2000 through two European winters, I am able to agree that brake ice can occur when using the wheels as speedbrakes in unsuitable circumstances. Also, de-icing fluid is sprayed into the auxiliary-power-unit intake. These do not fit the description of "main problems", however.
The "problem" with the aircraft is its high speed - sometimes, the cabin crew will note that there is not enough time to clear the cabin after service on short European sectors.
Source: Flight International