I didn't realise groping wasn't an offence in Germany :(
That said, BetaDad is actually speaking the closest to the truth here. The evidence doesn't point to this being recent immigrants. Immigrants, yes, if you consider 2nd/3rd generation immigrants to be immigrants (and if you believe this then 90% of the population of America is immigrant...) And perhaps some recent immigrants, too, but not overwhelmingly from what we know. Which isn't, as yet, very much. And while the crowd was large and still overwhelming in number it was not 1000.
Sexism in Germany is in some ways more backward than the UK and in some ways it's more progressive. We have a female head of state and many of the ministers are also female. The mayor of Cologne, BTW, is also female and has been attacked for her views but continues to uphold her role. Attitudes also vary hugely between areas. Some of the more rural areas are very keen on stay at home mums but in many areas it's becoming much less the norm. On the other hand Germany is the sex work capital of Europe, it's overtaken Holland.
My gut feeling from reading witness statements, articles, etc, is that the police force in Germany are typically very lenient/gentle based on the assumption that most people respond to reason. In this case, more robust management was needed but because it was the first incident of its kind (police chiefs are quoted as saying it's a "new kind of crime") they just haven't had the things in place to manage it.
There is definitely NOT a sweeping under the carpet, nor is the "advice to women" the ONLY strategy being implemented here. It's being criticised by German feminists, too, BTW, but it is in line with advice about other terror attacks with perhaps the difference being staying out of arm's reach of strangers (which is impractical, anyway). They are also sending in more security staff to train stations and installing better CCTV.