Not sure what kind of trail riding you like to do but here's some of my favorite locations.
-Willamette Mission by Brooks. Easy, mostly flat (as it's by the river) and really close in. Does cost $5/day to park there or you can get a season pass for $30 that also works across the state.
-Silver Creek falls outside Silverton, another pay for day use area that is covered by a season pass. Gorgeous scenery, nice selection of trail lengths and camping.
-Best for beach riding is Bob Straub park in Pacific city. You can ride the beach and has sandy trails going through trees, grass and ponds for water practice. Good for year around riding as you don't have to worry about mud.
-Bit farther away but darn good trails and camping facilitiers, quick google will tell you how to get there. Whispering Pines, Graham Corral and Sheep Springs. Or you can just find a place to pull over that has water available and put up a highline.
-Big Lake on the way to Bend. Some camping areas up there but I've found it's better for day rides. Plenty of snowmobile trails to follow and can get up on the Pacific Crest trail.
Several active horse groups in Salem but if you join OET they give you a trail book as a gift Oregon Equestrian Trails
. Not a member myself but know quite a few people who are. I keep thinking I'll join just for the book but I'm not really a club joiner.