pickle, yes they definitely happened.
But, prompted by your post, I checked to see what Snopes had to say. And it's interesting. Whereas normally Snopes just says something along the lines of factually accurate, may be true, unsubstantiated, definitely fabricated... here it offers no overall assessment. Instead it offers us a version of what I now think of as the Jess Philips lack of analysis ("worse things happen in Birmingham New Street on a Saturday night") namely "we all know male sexual violence and street harrassment is endemic, there's no reason to think there was a cultural explanation for these events or any sense that they weren't business as usual." In other words, the refusal to discuss and analyse that the Guardian and BBC were guilty of.
Incidentally the "worse happens in New Street" minimisation is one which spectacularly fails MrsTP's tests: often said by lefty dude-bros who didn't give a shit about that until they wanted a reason to ignore the Cologne attacks. (on this charge, I except JP herself who has a long and honourable track record of fighting male violence - I think this was a lone, if very bad, mistake on her part).
FWIW I think there is space for a detailed cultural analysis. There's a whole load of questions I'd like to see raised.
Were the Cologne attacks an example of Taharrush Gamea, i.e. not merely opportunistic sexual assaults but part of a world view which sees sexual assault as a way of policing women's behaviour and limiting their access to the public sphere? (There were some good analyses of this by Egyptian feminists and political writers of both sexes in connection with the use of sexual assault during the Tahir Square).
How, if at all, does Taharrush Gamea differ from institutionalised sexual violence in western culture, such as gang rapes in frat houses on American campuses?
What does it tell us about wider German culture? Is the square outside Cologne station becoming a no-go area for women in any way different from the fact that there are signs on lamp-posts outside the red-light district in Hamburg telling women not to enter unless they are sex-workers? What should be a public space, denied to women because of the threat of male sexual violence. Why, at the time of the attacks, were most of them not actually crimes under the German criminal code because at that point (only rectified last summer) rape and sexual assault were only criminal offences if you could demonstrate that you'd fought back - failure to fight back physically was deemed to be consent (even the word "no" was not enough)?
Without a decent analysis of these questions the left renders itself powerless in the face of racists like the one I encountered online last week who said "immigration is turning Sweden into the rape capital of Europe" (of course, it's not, it is mostly an artefact of the fact that the Swedes catalogue the stats round sexual violence much more rigorously than anyone else - but in the face of reports that they also do not record the ethnicity of the perpetrators for fear of stoking racism, it becomes hard to come up with really sound knock-down arguments).