Thanks again for all the replies. I think, based on your comments, I figured out what happened in my 10k map with 5k equator distance:
I was wrongfully assuming that I spawned on the equator but as Streetwind mentioned you spawn at 45 degrees latitude, meaning half way between north pole and equator (at least if you decide to spawn in temperate climate)
That is why I never could find the south pole on my map. I needed to travel 2,5k to the equator and then another 5k to the south pole. But from where I spawn, my map only offers 5k into each direction, so I passed the equator and ended up in the same climate zone I started in but in the southern hemisphere. South pole was cut off.
The following picture should illustrate what happened. Do you guys agree or is there a problem with my logic?