Finger patterns for playing chords - beginner question
Chord/melody modern style playing discussions
These are not actually beginner questions and they kind of open up that proverbial bag or worms.
The way I look at it is that I need all the help I can get. Both my pinky and thumb are invited to the party. You are right that some dulcimer players (such as Stephen Seifert) never use their thumb. Others (such as Guy Babusek) use their thumbs a lot and never use their pinky. As I said, I use both, and I let the context determine my choice.
My golden rule is to minimize movement. So as I move from one chord to the next, I try to have at least one finger that stays on the same string, so that you slide into a chord rather than having to lift up your whole hand and reposition it. Sometimes that alone will dictate what fingers you use.
As for the barre chord, most people use three fingers, either their middle, ring, and pinky or their index, middle, and ring. The only person I know of who only uses his pinky is Aaron O'Rourke. He barres with his pinky and then has three fingers for fretting strings. However, his dulcimer has a radiused fretboard made exactly to fit the curve of his finger. If you were to try to play like that I think it would hurt. Stephen Seifter barres with hisring finger backed up by his pinky. But as I said, almost everyone else plays the barre chord with three different fingers.
One thing to consider both regarding whether to use your thumb and regarding which three fingers to use for the barre, is how the dulcimer is positioned on your lap. If you play with your thumb and you play the barre chord with your index, middle, and ring fingers, you are going to want to angle the head of the dulcimer far out over your knee. If you don't use your thumb and you play the barre with your middle, ring, and pinky finger, your dulcimer may still angle out a bit, but the head will be closer to your body and the dulcimer will be closer to perpendicular to your legs. This is simply an issue creating a comfortable angle for your left hand to attack the fretboard.
Having said all this, Ken's points below are basically right. You need to find a way to fret the strings so that it's comfortable to you. If you find yourself contorting into all sorts of weird and uncomfortable positions, stop what you're doing and find a way to fret those strings in a more comfortable manner.