I finally expanded into some forested regions, and I see that units - even slaves - get a 'tree' icon above their head when moving through a forest.

Are modifications to movement and/or combat in effect when the icon is showing?

I finally expanded into some forested regions, and I see that units - even slaves - get a 'tree' icon above their head when moving through a forest.

Are modifications to movement and/or combat in effect when the icon is showing?

The mouseover says that the viewing range is decreased. Zoom out to confirm it. I know of no other effects though.

If you take a cue from most other wargaming, densely packed troops like hoplites and phalangites should suffer penalties in combat, as should cavalry. I would think, if you wanted to go crazy, you'd give troops a foraging bonus for camping in the woods too! Peltasts and levy spearmen should be at home fighting in the woods, whereas cavalry and heavy infantry should want to avoid it at all costs. Lightly armed men can pick on the scattered formation of the cavalry and infantry, and retreat nimbly when the enemy regroups.