Diana, the Roman numerals that we use to refer to chords have nothing to do with fret numbers. We use those Roman numerals no matter what instrument you are playing. Referring to Roman numberals for chords allows us to transpose from one key to another. In the key of D, D major is I, G major is IV, and A is V. In the key of C, C major is I, F major is IV, and G major is V. That is the case whether you are playing the dulcimer or the piano or just talking about music and describing the chord changes of a song. Again, it has nothing to do with frets. Instead, it has to do with the chord associated with each scale position. If the first note of our scale is D, then the fourth note of the scale is G, and the G major chord will be referred to as IV. If we wanted a minor chord associated with a scale position, it would be written in lower case Roman numerals, as in ii, or iv.
And remember that even in a DAd tuning, we might not play in the key of D. I just arranged a simple version of "WIll Ye No Come Back Again" in the key of G but tuned DAd. The G chord will be the I and the C the IV and the D the V. Note how those Roman numerals are determined by the key of the song and not the fret position.
I have to admit that I mostly play in 1-5-8 tunings. But I usually tune DAd or CGc on my standard dulcimer, occasionally going up to EBe. And I tune AEa or GDg on my baritone. When I play chords i don't think "now I'm moving from G to C." . Rather, assuming I'm on my baritone tuned to G, I think "now I'm moving from I to IV." That way I don't have to think about how my dulcimer is tuned and don't have to do any fancy transpositions. I just play the same on any instrument in any 1-5-8 tuning.
There are plenty of chord charts floating around the internet for the more common dulcimer tunings, so you can easily find chords to play when you are tuned DAA. Check out the attached file by Stephen Seifert, for example.
updated by @dusty: 12/15/16 04:32:25PM