I'm a bit confused - why wouldn't it have been under a ton of ice? I thought most of the northern hemisphere was under ice at the time - but from the description it sounds almost temperate.
Alaska was never really fully under ice. If you look at this picture of the Laurentide ice sheet [1] during the last glacial maximum [2] then that shows the most Alaska was covered in ice which was 26 to 20 thousand years ago.
The time frame where the Bering land bridge is being looked at for the OP article is a wider 36 to 11 thousand years ago.
The notion is that most of the water was held in higher altitude (than sea level) glaciers across interior mountainous regions of the major continents leaving the polar sea extents much as they are today albeit with lower sea levels.
And even if it wasn't glaciated, there should still have been winters where the lakes would have been less of a barrier and more of a clear path to walk..
