I like this topic, as it has me really thinking about this.
My first thought with "vernacular" and golf was the Australian Sandbelt. Then after reading a little bit of the wikipedia article, I thought maybe it's too "designed" and only places like the UK links or Some Guy's Backyard really fit. But then reading more in that same article, I think it really does fit. Those sharp edge bunkers, those firm conditions, and the design decisions made from them, are all highly influenced by local materials--the fine and compacted sand in this case. Also, the incorporation and blending of the surrounding native scrubby plant textures.
Following along those lines, you could argue for the vernacular of many of the early Golden Age courses of the Northeast US and their use of chocolate drop mounds and berms to bury stones as well as push-up greens to keep the heavier native soil from getting too saturated. Also, more grass-faced bunkers to avoid dealing with washouts from summer storms.
The region I struggle with a little more is California and the heavy influence of MacKenzie and Billy Bell/George Thomas's flashy sand bunkering. Even that movement though could be traced to a response of natural conditions--Cypress Point and its dunes and sandy soil, obviously, and the Thomas LA courses, which, while not necessarily all that sandy, were on properties laden with exposed soil from washes both high and low, lending themselves to bunkering that could match up to that. Also, the bigger topography and lack of trees of many courses in CA lends itself visually to bigger, flashier bunkering that better fits the scale of the land. But, in some of my general research and understanding of golf's stylistic evolution here, I'd contend that many places have *followed* the style of the big courses vs. responded to natural conditions present. Annandale, which employed much more of a formal/grass-faced bunkering style to start and converted to a Bell flash style not long after, could be an example of that. But even then, you could make an argument about what is more "vernacular." Perhaps the original style is more "vernacular" in its utilization of (what I am assuming is) a heavier soil, but could you argue the Bell style is more "vernacular" because it better visually responds to the neighboring hills and barrancas running through the property? It's fun to think and argue about.
In the end, as golf is a naturally borne game and one that exists outside in the elements, there is almost always going to be some level of "vernacular" to the design. The degree of which it exists probably will tell you something about the experience you can expect when playing it.