Be really sweet and friendly to hikers. Stop and and have a chat. Dogs are probably a greater hazard to mountain bikers than they are to dogs. Some horses freak out, kick back, dump their riders, etc., when frigthened. So be careful when meeting equestrians.
Some routes cross pasture lands.
Make sure that you carefully close all gates that you open. Do everything possible to avoid looking like anything even vaguely similiar to a moose in October and early November, unless you like to get shot. There are several areas that offers excellent MTB-trails around Uppsala. The descriptions here are in Swedish but can easily be used by non-swedish speaking people. The maps and the gradings will be sufficient to get you started.