How to Get Dark Wood in Moonlight Peaks

Quick answer: chop the white-leaved Weeping Willow trees in the Howling Marshes with your starting Rusty Axe. You can also chop the large fallen logs around the farm and other paths after upgrading to a Copper Axe. Put 3 Dark Wood into a Refiner to make 1 Hardwood Plank.

Every Dark Wood Source

Source	Where	Tool required	Best use
Weeping Willow	Howling Marshes	Rusty Axe	Fastest early repeatable route
Large fallen log	Farm and other outdoor paths	Copper Axe	Clear blocked land while collecting Dark Wood

Weeping Willows have pale or white leaves and long branches that droop like vines. Do not confuse them with an ordinary tree that only drops Wood. If you have already cleared the visible willows, use the log route or return to the marshes on later nights.

Fastest Weeping Willow Route

The Howling Marshes sit north of town and east of Moonlit Pines. The shortest approach is:

go to Town Hall;
take the path along its north side and continue east;
turn north into the Howling Marshes;
look for the pale, hanging canopies around the raised islands;
chop each Weeping Willow with the Rusty Axe and collect the Dark Wood.

A second entrance runs east from Luna's Seed Stall in Moonlit Pines. The Howling Marshes guide has both routes, its quests, full-moon events, fish and Critters.

Large Logs and the Copper Axe

The large horizontal logs around the farm and outdoor paths are the second Dark Wood source. A Rusty Axe cannot break them. Buy the Copper Axe from Ridge at the Howling Hammer for:

1,000 Coins
1 Rusty Axe
3 Copper Bars

Smelt Copper Ore into Copper Bars at a Furnace. Upgrading is worthwhile even if willows are available because clearing the large logs opens more usable farm space while building a Dark Wood reserve.

How to Make Hardwood Planks

Repair the bridge during A Bridge Too Far to unlock the Refiner recipe, then craft the Refiner at a Workbench with:

20 Wood
20 Stone

Load 3 Dark Wood into the Refiner to produce 1 Hardwood Plank. Check the exact number of planks required by the current quest or blueprint before refining the entire stack; some objectives may need a raw material rather than its processed form.

Weeping Willow Respawn After Patch 1.1.45

The official July 21 patch notes say version 1.1.45 increased the chance of Weeping Willows respawning in the Howling Marshes to improve late-game access to Dark Wood. The note also says more improvements are planned for version 1.2, but it does not announce a 1.2 release date.

The patch improves the chance; it does not promise that every tree returns the next night. If no willows are visible:

confirm the game has received the current patch available for your platform;
sweep both sides of the marsh islands rather than only the Town Hall entrance;
harvest large fallen logs with a Copper Axe while waiting;
revisit the marshes after advancing several nights.

This Is Not the Mysterious Bay Fallen Tree

The quest tree for The Mysterious Bay is a different object. It blocks a waterfall in Moonlit Pines near Luna's Seed Stall and is removed with the Arborascend spell; it is not the Dark Wood route in the Howling Marshes. Follow the fallen-tree walkthrough if the journal says to lift a tree.

Sources

Marvelous Games — Moonlight Peaks Patch Notes, July 21 — official 1.1.45 Weeping Willow respawn change and 1.2 wording.
GameRant — Dark Wood and Hardwood Planks — both Dark Wood sources, tool requirements, Copper Axe cost, Refiner unlock and recipes.
PC Gamer — Fallen Tree Location — the separate Moonlit Pines quest tree and Arborascend route.
Moonlight Peaks Wiki — Howling Marshes — current location description and forageable cross-check.