The reason for the frozen area is found in the Frost Temple.
The map shown is an artist rendition and may not be entirely canonical (though there is no canonical map outside of what is in Age of Conan), however it gives a pretty good indication of where everything is in relation even if not quite to scale. So the coastline may not actually be an ocean or even large inland sea, but a large uncharted lake.
This was done for mechanical reasons for the purposes of lighting. I wouldn’t consider this canon to the story. Much like the fact you can carry 200 thralls in your pocket.
As for the biome diversity in close proximity, I would hope not. The Exiled Lands are enchanted. I would suspect the ghost fence keeps in more than braclet wearers. But also affects much of the climate. If you look at the Maproom you can see what the Exiled Lands were before the Sandstorm was unleashed during the last days of the Giant-Kings. Most of the Exiled Lands were not desert originally.