In the next update, Druids and Rangers will have an alternative to chopping at trees, here's how it works:
Start a campfire near a placeable tree (you must be within 10 metres), when you click the campfire you will see the option to Forage For Wood. A calculation is made based on your Search and Spot skills vs. a DC 30. (d20 + Search Skill + d20 + Spot Skill vs. DC 30). If you succeed you will find 2d4 branches of the wood that grows nearby.
You can only do this once every 90 real life minutes. You will also not be able to do this while Invisible or under any forms of Sanctuary.