Sorry, went to sleep for a bit - uploaded the entire world to mediafire (I hope you have 7zip installed)http://www.mediafire.com/?ul0rtfkc20ge1ve
There should always, always be at least some regions of every type on every continent. Most likely they are down south of the water or something of that nature.
The entire south area is inaccessible, as you can see from that picture. The only way to get to it is through a boat, but the port has stormy weather and it's impossible to board any ship there without clearing the storm first. But to clear the storm, I need a level 3 Aquamancer well, which requires cedar logs to build, so that's a catch-22. Note that I did not waste cedar logs meaninglessly - I found 22 in total, then I built the residential building (10 logs), the stonemason's building (10 logs, requirement for aquamancer well) and am still short 8 logs for the well itself. If I had built something irrelevant, the situation would be even worse.
I also checked the wiki, which suggested that "cedar logs can be found underground in caverns". I went hunting for 2 hours in the abandoned town caverns and found absolutely no cedar logs.
"In caverns, there's even more: granite, quartz, and other goodies abound. There are sources of cedar logs and of refined lumber. Way more consciousness shard caches, in general, per cave. "
As far I know, this is actually incorrect. I do try to troubleshoot my own problems before bringing them up.
If you get our door missions on those areas (battlegrounds, boss towers, and so forth) the areas that spawn will also include trees that you can harvest for cedar. They are essentially infinite since you can cancel the mission to "fail" it then start it again and it'll get a completely new instance you can farm.
A recent patch changed it so that overworld door missions don't spawn in stormy areas. Those 3 city areas are stormy, so that doesn't work. There were some door missions, but I cleared them all looking for cedar logs, since I didn't know about this. Can't re-enter.