So a forest may give only a 20% reduction to a tanks attack value, but it should give something like +50% bonus to hard attack values of the defenders.
The idea is nice, yet Clausewitz lacks the ability to boost individual values.
Btw: different penalties depending on softness are already applied, because penalties are equaled amoung all modifiers along the division.
It might have been said before and I missed it, but in a Forest there is no way that an Armoured Division should take casualties from a regular Infantry Division. You cannot blow up tanks with rifles and hand grenades but you can still be blown to bits by blind tank fire moving in radians.
You can in fact kill tanks by using grenades. A common example is the grenade bundle, thrown at a track it had a good chance to immobilize the tank, placed at the right point you could even blow the vital parts so the crew has to bail.
Tanks are
"eggshells with hammers" - and while they have superiour firepower, esp. on range, they often lack short range protection. So you want to keep them away from your enemy. Even a tank with a turret is totally helpless if infantry gets close, basicly you can jump on its hatch and it can't do much about it. A commen early AT tactic was for example to blind a tank in melee by cracking the external mirrors or even just laying linen over them. Thats why tanks are extremly vulnerable in cities: One bazooka or panzerfaust shot from a winow at close range and *boom* goes your tank. And from upper floors you can even aim at the weak top armor.
To reduce this weakness, tanks got additional MG guns (like the remote controlled Hetzer MG) and close range mortars (like the german Nahverteidigungswaffe), but tanks are always prone to close range assaults, esp. in the heat of battle and when lacking protection from combined arms assistance.
And about the forest, well, there are two things to keep in mind:
First, if tanks drive into a forest, they have very limited LOS. They will probably see about 10-100m deep, depending on the flora around them. In short: They are blind.
So in general, if the whole province was full of forests, tanks should suffer even higher penalties on offense and thoughness.
However (second point): A "forest" province does not consist of 100% forests, so the tanks actually don't have to drive into one. They can't fully utilize their attack power and the defender gets a defence bonus, since some forests inside the province aid the defenders.
This also the reason why ART has a penalty in forests instead of a bonus: In reality mortars and other ART fire were esp. dangerous in forests due to treebursts (ever had a tree explode above you and send hundrets of wooden shrapnells at your face?)...
The technicalities are no doubt nigh on impossible to code but normal infantry should not be damaging panzer formations in any terrain.
Normal infantry carries AT weapons in HoI3. They have small calibre AT, like AT rifles and 20-50mm towable AT guns, as well as grenadebundles, satchel charges, grenades, sticky bombs and alike. So they have the ability do attack tanks, both on long and short range. However, they are ineffective, and thats why they have only ~1/4th of their SA in HA.
edit: @espen below:
