The Black Forest isn't actually that difficult. If you don't have it already get:

• Leather armor and a cape.
  
• Craft a bronze axe, which is generally good for combat in the Black Forest and you can use it to chop fancy woods.
  
• Craft a wood shield (you can customize the color! Look at the top of the crafting screen for a button called "style" under the item name!) and upgrade it at least one level. This allows you to parry skeletons with swords and block arrows.
  
• Get fine wood and craft a finewood bow and fire and flinthead arrows. That will allow you to fight and kite trolls (a crude bow works too).
  
• For food berries or honey + cooked boar and deer meat is enough for pretty much anything in the Black Forest. If you still struggle with HP/stamina get tin and build a cauldron, which allows you to cook better food.
  
• Don't go out at night. You will get swarmed.
  
• Consider to surround your base with stakewalls, otherwise the "The Forest is Moving" event might get a bit annoying, especially when they go for your carrots or other structures outside.

If you get the first three things (leather armor, bronze axe and upgraded wood shield) you should be fine.