The answer isn't in their armor the answer is in their tactics and the terrain they have to fight in.
There are a number of issues in your question. Firstly no late medieval army in history ever consisted purposely of heavily armored knights! Not only because those knights needed support personnel to maintain their horses, camps, armor and weapons etc. But also because the late medieval armor you describe was fantastically expensive and only ever worn by the elites of society since they were the only ones who could afford it. Instead the vast majority of 15th century European armies consisted of massed pole arm equipped infantry wearing lighter/cheaper armor, crossbowmen or arquebus (primitive firearms) armed troops, light cavalry when available and an artillery train consisting of crude muzzle loaded cannons firing stone or iron shot and finally some (as many as could be gathered) heavily armored knights! And those knights? Primarily used lances when mounted and pole arms when not because those were the weapons that could pierce or puncture armor like their own!
Secondly because given the terrain you've stated the fighting will be occurring in i.e. forest (presumably with its fair share of hills, valleys and marshes & rivers etc) I cannot image a worse choice of armor for a soldier to be wearing. Put simply Gothic plate armor was NOT designed for use in close restricted terrain like the forests you've described. Instead they were designed for massed combat in relatively open terrain. This was because the high level of protection afforded by Gothic armor came at the cost of weight & restricted vision and hearing (with the visor closed). Compared to your barbarians? A regiment of gothic armored fighters armed with pole arms walking in formation into a forest would, as individuals be at an extremea great disadvantage in terms of hearing/seeing and movement as individualswhen it came time to fight anywhere near as effectively as. At least when compared to how well they could inwould do on open ground.
Lastly, your barbarians. They're not encumbered in heavy armor and or helmets that restrict their vision and hearing but are armed with lots of heavy (Conan the barbarian style) choppy,choppy stabby,stabby weapons designed to pierce heavy armor or slip between it's joints like battle axes, maces, war hammers & short spears to attack joints - what a coincidence! They also know their home and it's terrain intimately (every fold in the land every thicket, every stream and hill) while presumably their invaders do not! Finally also they are used to fighting in massed groups or as individuals so they'll be as effective in small groups staging ambushes as they would be in larger fights. Knights weren't really trained or equipped for ambushes.
All of which combined means your barbarians (if they are also smart and well lead) can ambush, raid & harass your knights while only choosing to meet them in a massed battle when and where they chose tothink the time is right i.e. when they have the advantage not the knights. A (very loose) example would be the battle of the Teutoburg Forest, the Germanic tribes and the Roman Legions who fought there.
Conclusion? If your invading army does consist entirely of gothic knights? Those knights are toast.