I used to live in Colchester and near Halstead, but tended to roadtrip to Thetford. Otherwise Danbury is pretty good and the highest point in the county. Alternatively, near Southend you've got Hockley Woods (lived there as well).
You'll rarely have to avoid horses if you take the (excellent) singletrack and keep away from the poxy fire roads. Everyone seems to meet at the teat hut up at High Beach and anyone there can point you in tthe right direction. I ride there 3 times a week. Good thing is you can't really get lost, per se, since the forest is surrounded by road on all sides. If you just kept going in 1 direction you'd come to a road eventually. Contrary to what JoeHan said there are plenty of hills and fast, rooty descents if you know where to look. It's very technical in some areas, due to erosion and dense forest, and due to the high clay content in the soil it can be pretty slippery most of the year round. It will also ruin your bike if you don't look after it - Trust me.
EF has a pretty bad reputation, but it's generally slated by those who haven't found the best bits. If you want to hook up with people riding the trails then a good place to start is: www.eppinghardcru.co.uk
There are countless groups of familiar faces I see around each week and pretty much all will be happy to have someone new coming along so don't be afraid to ask.