While a chord's quality (major, minor, diminished, etc.) is the primary factor in determining how it "feels", the context around it also plays a significant role. You are absolutely correct that the Ab, Eb and Db in your example feel a little less bright (a term I greatly prefer over happy) than an isolated major chord, but this has nothing to do with them being flat.
Instead, it is the preceding Fmin that sets a certain precedence, suggesting that we are in a minor key, and effectively darkening the entire progression. If you leave the Fmin off and only play Ab->Eb->Db they will sound a little brighter. Similarly, is you shift everything up a half step so you are no longer playing flats (F#min->A->E->D) it will have the same quality as your original progression, despite the lack of flats.
On their own, all chords of the same quality sound exactly the same (with identical tuning and ratios) and this is essentially the point of equal temperament tuning. A major, played on its own, will not sound any brighter or darker than Ab major. However, no music consists of a single, isolated chord. The voice leading surrounding any given chord changes its effective brightness. Once a contextual precedent has been established, chords of the same quality can have differing levels of brightness.
These interactions can be incredibly intricate and subtle, but, in many cases, lowering pitches can, in fact, darken the overall context and thereby each individual chord, so you're observations are not unprecedented. That said, be careful not to equate a lowered pitch with a flat note; flattening natural notes will have the same effect as naturaling sharp notes.