You shouldn't try to go to the mountains without at least some iron armor. The biomes order goes from Meadows-Black Forests-Swamps-Mountains-Plains.
It's possible to go in with copper, just very unsafe. If you must go into the mountains, either play carefully(or cheesy) and snipe the wolves with some arrows.
I went into the mountains with fully upgraded Copper pants + helmet and a fully upgraded Iron chest armor and managed fairly well.