Black Wood is superb, and no-one goes there. A hidden gem. For combined quantity and quality of singletrack, I don't know anywhere else in Hampshire that comes close. The annual moto endurance is this weekend (24/25 April 2010). Get up there during or soon after, and follow the track around (over 13 miles). It is often damp in there but I don't remember it ever being sticky, just soft. There are some vehicle tracks in the SW corner that flood. I think the entire route is covered by tree canopy, so it will never completely dry out. Also in the SW area is some interesting singletrack that is not part of the m/c enduro course. Black Wood is definitely Forestry Commission, and there are no signs saying no cycling. So few people use the woods that you're unlikely to annoy anyone, or even see anyone.
Micheldever Woods has a wide-ish singletrack running up the east side of the gravel road, a bit unexciting when dry, much better when damp. Coming back south down the gravel road, turn off right to the west, about half way up the long incline, then you can pick up a narrow and winding track to the left (after 50-100m?)(there is a big bomb hole a bit to the right) taking you back south, with a wider fast downhill runout right back to the car park. You'll cross a few other tracks and if you explore along these, you'll find some more tracks. Enjoy!