Is this an earth-sized planet (40000 km circumference)? If so, the north pole is going to go right on that little plain north of the great forest if that continent is indeed 10000 km in latitude extent. I've added some distance lines for reference to your map and attached the results. For a 40000km circumference world, rhe horizontal lines are the equator (0), 45 degree latitude, and 90 degrees latitude (pole). There would be undoubtedly be some projection effects on there that would make the lines not straight, but it's enough to get the idea. The location of your forest would be in the arctic ocean or in antarctica if it were here on earth. My math is suspect at the best of times, but I think I'm close on this one (40000 km total, half for a hemisphere, half again for equator to pole - should be 10000 km).

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If the mountains in the north are a frozen wasteland, then the simplest explanation for the forest simply involves heat to melt ice. Admittedly, there usually isn't a lot of moisture in the really high latitudes because it mostly freezes out before it can get there. Weather pattern would be key here and you'd need a larger map to show other (if any) continents to get a good picture of those patterns. Of course, if this is the only continent, then there will be some really spectacular storms that could dump a whole lot of moisture on those mountains. Enough moisture and the glaciers will march down out of those high polar mountains and melt when they hit the volcanic province that is responsible for the large area that the forest sits in. It would play hell with the other cultures that you had in mind for the surrounding areas, but it would be very scenic.