Woodland is largely considered to be no good terrain for tanks, but that's only partially true. Tank forces made much use of woodland (including the famous dash through the Ardennes in 1940) for resting, as marshalling areas and for concealment. ATGMs are no threat in woodland, for example.
Flat woodland with young trees offer little resistance to tanks 30+ tons heavy with 400+ hp power - particularly if the roots are deep. Flat roots may push upwards to the belly and cause trouble while deep roots stay in the ground when a tank rams the tree.
|T-34 passing through woodland, 1945|
These training videos show tests (mostly done with Leopard 1 tanks) about the ability of MBTs to pass through woodland, including the effect of slopes:
Stronger trees tend to grow with greater spacing, and often allow tanks to pass in between. Only a few of them would need be cut down to allow passage for MBTs or even cars.
|Typical German forest aisle|
Eastern European woodland is very different from Central European woodland, with greatly different consequences for mechanised forces' manoeuvres.
Central European woodland is often very hilly (typical German woodland is on hill top and crests), has many unpaved forestry roads and to limit fire hazards there are many forest aisles.
Eastern European woodland meanwhile is largely flat, and as the videos above showed, this makes a huge difference. There are different trees as well, but I'm not well-informed on which exactly.
So the relevance of Eastern European woodland as obstacles may differ greatly from Central European ones'.* I'm not aware of any doctrinal or equipment adaptation to this on part of the German army. Maybe we should pay much attention. The following video is interesting:
There is actually such a thing as a forestry mower.
A kind of lawn mower on steroids, to cut through woodland:
It is imaginable that armoured engineers could cut through most Eastern European woodland at a walking pace or more, leaving behind an unpaved (or even paved!) road for combat and supply motor vehicles of all sorts. Even plain tank battalions might be quipped to move at a bicycle's speed through woodland with stems of up to 30 cm diameter (deep roots).
Such efforts would be loud and may attract artillery fires, but they're nevertheless really bad news for everyone who hopes to gain any defensive effect from woodland in the Baltic countries, for example.
Maybe the tank and engineer troops in NATO countries should be equipped and trained differently in order to adapt to Eastern European woodland characteristics, but this might take a long time. The West German army's requirement for a mine sweeping tank (using a technology improvised in 1942!) took almost 35 years to produce an operational capability and that need was much more self-evident.
*: Similar with rivers and lakes: Those tend to freeze over and allow even vehicles to pass much more in Northeastern Europe than in Central Europe.