Even for the most environmentally-friendly, conservationist player, I suggest Chopping some Forests.
In real life, too much forest growth can cause a forest fire to be extremely devastating, as the fire can affect an extremely large area of land. Admittedly, humans are terrible on forests and we chop far more than we should. But, a tiny amount of chopping can be better for a forest than none at all.
As for your game, I suggest at a minimum chopping the Forests that I have surrounded with red squares. These Forests are contributing zero regrowth possibilities. By chopping them, you actually increase the overall chances of Forests regrowing in your game, thereby netting you free Hammers and, if keeping Forests for Lumbermills or Forest Preserves is your goal, will give you sufficient time to regrow most of them naturally while allowing you to use Forest Preserves to regrow the rest that don't regrow in time.
If a Forest is surrounded by horizontally and vertically adjacent squares which cannot have a Forest grow on them (including squares that already have a Forest on them--in terms of the game, you can't grow a Forest over top of another Forest), and if such a square has at least one horizontally or vertically adjacent square with a Forest in it, then such a square is ripe for the culling. You should strongly consider Choppnig such a Forest; unless Chopping one of the adjacent squares is a better choice, you should Chop that square's Forest in the early game, giving it plenty of time to regrow.