There are no real guidelines regarding climates mostly because people were interested in mapping more than figuring out if the climates on their map made sense.
Also, we have no idea how much Earth-like this world is or if it is even a planetoid. Just go with what make sense to you.

But if you want my opinion, yes it's going to be cold and humid.
No extreme cold because it should have a maritime climate for the most part.

Starting with the northernmost part of the country, the warmest:
I think the climate would be similar to the climate found in Northern Scandinavia, tundra. It's closer to the pole but Europe receive the warm waters of the Gulf stream. The influence of the Gulf goes as far as the Barens sea. Therefore, Europe is warmer than most other places at the same latitude.
Unlucky for you, to my understanding, most of the warm water from the equator would be diverted south when the current reach the coast of country 57 (based on the zoomable world map).
Therefore, you don't have that warming effect that Europe enjoys.

So a more appropriate example might be the climate of Southern Patagonia, also a tundra. They do have quite a bit trees around Ushuaia. So it could be ok for a civilization to develop there. Thought a modest one since the vikings developed under somewhat warmer climates. Actually, you have the advantage of having warmer winters in comparison, I think.
That would be my realistic yet realistic estimation but one part of me tells me that it's probably colder than that.
At 62°S, we have King George island. While still a tundra, is much less hospitable. So it is probably somewhere between the two.

The south is close to 70° maybe more. And that is definitely an Arctic climate. Too cold to live there.