I'm not sure how well they've lived through the last couple of very hard winters, but they've been here wild since the 70's so they've already survived hard winters. It's no 'infestation' though - they are spreading, but slowly.
Our numbers seem to have decreased somewhat in the last few years. I don't know if the West Nile Virus that reduced the populations of many bird species around here gave them an opening. Apparently these parrots were fairly immune to it. But now that the virus seems to have run its course, and the native species have repopulated, we don't see quite so many "Monks" as we used to. Their proclivity to want to build their huge colony nests in cellphone towers led (despite public protest) to a number of extremely drastic forced 'evictions' - which also contributed to reducing their headcount.
There's still plenty of them around however. *skraaagckkk!*