DA Morgan quote:

"Some of those frozen mammoths were found with green grass in the mouths and plants from temperate climates in their stomachs."

People who have studied the vegetation on the ancient tundra agree that it was a mix of what are now warm and cold-loving species. Many plants now found only far to the south were present. The interpretaion is that the tundra was an example of "mosaic vegetation". Microclimates allowed warmth-loving species to survive. It's possible the extinction of the large herbivores caused the disruption of this pattern. Anything written by Paul Martin or Tim Flannery should cover the topic but I'll see if I can find a site.