A global winter wouldn't completely block all the sun light. There would still be some. So some plant life would still survive. If it was kinds that the smaller diversity of the large herbivores couldn't eat then they would die off. If there had been a great diversity of large herbivores then the chance that some of them would survive would be greater. That is because the diversity depends on their living in different ecological niches. Probably eating different plants. So if those different ones had survived then a chance for some of the carnivores to survive would have been greater.
And of course this has to be taken with the usual caveat that neither one us really knows for sure what we are talking about. This is just the way it seems to me, based on what the author of the story I linked to said.
Bill Gill
