WOW, RMH!! You've just named the parts of town where I was born and raised...do you live in Happy Valley?
My mother and sister still live on Mt. Scott within the Happy Valley city limits. I went to Happy Valley Grade School and the original Clackamas High School (which was then in Milwaukie). My father (William C. Beutler) was the first fire chief of the Happy Valley Fire Dept and designed two of their trucks. He was also very involved when Happy Valley was became an incorporated into a city.
Until recent years, Happy Valley had many resident horses, but now I don't know if any live there.
In addition to the Mt. Hood Equestrian Center, I would also ask at Columbia Equine Hospital and Willamette Equine Hospital. Sue Roake of Bebop Farms in Boring may know of someone close in Southeast. Clackamas Community College offers riding classes at a stable nearby in Molalla, and if they don't have boarding, they would probably know of someone else.
If you go to the NW Miniature Horse Club list of area farms, you will find a breeder in West Linn...I'm drawing a blank, though, on their name.
If you are within the Portland city limits, zoning allows you to keep "livestock" so long as they are no closer than 50 feet from any house...after we did our paperwork (when my husband and I lived near Mt. Tabor), they told us that they don't consider minis livestock and that we didn't need to follow those rules.
I'll ask my sister if she knows of any boarding facilities in the Happy Valley/Sunnyside/Clackamas area and let you know. Beyond that, welcome to the neighborhood!