Arda does seem to have polar caps, though the southern cap is not located in Middle-earth proper, but near the southern tip of the continent known as Dark Land (also South Land). The lands of Forodwaith, including the Ice Bay of Forochel, would fall within Middle-earth's arctic circle. Dark Land looks like it could have broken up at some time to create Antarctica, Australia and Indonesia. The illustration below is based on a sketch of Arda by Tolkien that can be found in The Shaping of Middle-earth (Part V: THE AMBARKANTA):
Is this a cannon map?
Can the first picture be labeled? That's the second "whole Arda" map I've seen.
The first one is this
The map you've posted was a 'thematic' one drawn by Allan Curless for David Day's A Tolkien Bestiary (1979). It is not geographically accurate, nor was it meant to be.
I'm sure they do.