Watch out for dwarfs trampling saplings, of course. That's the main way which cutting trees would reduce tree growth. Play around with pathing costs; you could set up a grid of low-cost areas with restricted areas between, so that dwarfs would only go into the tree-growth areas when they have a task, and would try to stay in them for as little time as possible. Or something like that.
Be prepared to micromanage the traffic costs after you set up the grid (which itself is time consuming): when you want to deal with an invasion or a hunt, you want to switch your traffic costs to all be even. This has the adverse effect of ruining all the other traffic zones you've set up. Also keep in mind that trees take ~2 years to grow from sapling to tree.
Back in 40d when I was too inexperienced to venture forth to magma sites, I valued trees a lot so I went to the trouble of setting up an underground tunnel network just to avoid walking on the saplings. The tunnels would have to be 2 z-levels below the surface since saplings that don't have a full wall of soil beneath them won't grow further.
Now though, the underground (my worldgen ensures there is water in the caverns) and enlargened caravans supply with much more lumber than there ever used to be. Trees will grow everywhere (muddy or soiled and with wall beneath them) thanks to finding the underground water. Just don't reclaim - that gets rid of all the mud in the caverns.
Am I the only one who has clearcut huge swaths and gathered some plants out of them only to see them become virtually dead wastelands? Between dwarf traffic to cut and stockpile the wood and gathering plants my dwarves seem to leave bare soil patches which take years to regrow anything more than grass. It's almost as if my fortresses suffer from erosion or something.
You embarked on a high drainage area. That you had any trees at all to start with means you also had decent rainfall, but you're pretty much on camouflaged badlands. Just about any traffic will turn grass into barren soil and I'm not sure how plants grow on bare surface soil (they don't grow at all according to your anecdote). Hopefully DF2010's caverns nullify this problem, as underground trees are far less picky about where they grow.