You can actually see how it will look like by watching The Expanse - it takes place in ~2350 and there is a huge wall all around Manhattan including in front of the still standing original UN building, as most terrestrial glaciers are long gone.

But this is actually a much less pressing issue than the couple gigaton nukes the Mars Congressional Republic has targeted on Earth, the ever more emancipated belters and some very shady deals by secretive yet very dangerous corporations.