See that's the difficult part:
The Wall is made of ice, so it would not make sense for a giant frozen wall 300 miles wide to be admist green, lush forest. The Wolfswood does continue up to and slightly beyond The Wall, but I think this area of the forest is likely to be quite snowy still - something like
this, if it were real.
I think the snow in my WIP can definitely be lessened and spread out a bit, but I don't believe this area should be completely devoid of snow and ice, as depicted in Tear's map.