If we use North America as a model, I would expect to see:

In the coastal and low-lying regions of Lammoth and Nevrast, there will be a mix of maples, oaks, spruce, and firs, with the occasional beech and cedar. The further north one gets (or higher elevation), the firs will become more and more prominent. However, once one crests the Ered Lomin, the firs will quickly give way to pine.

I suspect you're thinking of aspen, rather than birch - while there are oddball species that prefer it the other way around, most aspens are high-altitude trees, while birches tend towards lowlands.

I'm not sure where the tradeoff between pine and aspen happens - I remember that some areas of western Colorado (especially around Grand Junction) are very heavily forested with aspen, but that's a good six hundred miles from the nearest ocean, and across multiple rather high mountain ranges. Just by looking at the map of Beleriand in my Silm, I would guess that Nuath would have either a pine/fir mix, if the weather came up along the ered wethrin from south of mount Taras (a long trip, but no mountain ranges in the way to pull out most of the rain), or it would have a pine/aspen mix, if the weather came down from the firth of Drengist (and thus over some serious mountains).

Considering that a large amount of the water in the Sirion comes from Dorthonion and Ered Wethrin, I would suspect it's the former - that's a lot of water to go up and over the mountains. Also, the size of the Gelion up north suggests that the March of Maedhros gets a decent amount of water. It would make sense to me, anyways, if all of Beleriand's weather came from the southwest, from the sea.

Or, I could be all wet. The Columbia river is huge, and its watershed is on the far side of the Cascade mountains (and the Olympics) from the ocean. Personally, though, I'd take that to mean that Hithlum should probably have a fairly big river for drainage.