Ronald, the Kens have already highlighted the most important obstacles: the chromatic fretboard, the placement of the bass string, etc.
I think the biggest obstacle you will have is string spacing. The strings on the guitar are placed much closer together than are the strings on the dulcimer. If you are going to play in a modern chording style in which you fret across all the strings, string slots that are next to each other (say the G, D, and A strings, for example), will be too close together for you to get your fingers in there. And if you choose string slots further apart (say the B, D, and low E strings), they will be too far apart and will make chording difficult.
If you want to play in a traditional droning style that string placement will be less of an issue because you will only be fretting (either with a finger or a noter) the string closest to you, so the strings won't have to be equidistant.
But regardless of how you proceed, as Ken states, the slots that exist in your nut and bridge may not work for dulcimer string gauges.
I would suggest another option. Keep your guitar in playable condition as a guitar. Find yourself a cheap cardboard dulcimer. None of them are that loud, but some of them are ridiculously nice and make me feel silly for spending so much money for fancy dulcimers made of fancy woods. Backyard dulcimer makes a kit and so does Folkcraft. They take about an hour to put together, or you can pay a little extra and have it pre-made. You can sometimes find used ones as well. Those cardboard dulcimers are more than adequate to get you started while you wait for your winter dulcimer.
Dusty T., Northern California
As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie
updated by @dusty-turtle: 11/12/19 12:49:40AM