I don't believe the Bering Strait area was subject to any recent (within the timeframe we're discussing) glaciation.
And there is always a leading edge of the glacier where all that ground-up goodness ends up. Many dynamic biomes are found on the boundaries of extreme and hostile environments.
Take a look at the wiki page linked above. Beringia was never really covered in ice due to the wind and sea currents near it when it existed. The area was a 'refugium' of steppe grasses and light forests. It is thought that people may have moved there, stayed there, and then moved back into Asia as time went on, as well as into the Americas. As for using the area to farm, the very short summer growing season of higher latitudes is not well suited for agriculture.
