It seems that the ratio of those authors allowing a field to be a Dedekind domain to those who do not is almost 50 - 50. Why such a bewildering lack of consensus for such an elementary notion?
Historically Emmy Noether's paper introducing the concept "Dedekind domain" certainly included fields (see e.g. Kleiner's book on the history of abstract algebra, which gives axioms). She was characterising the scope of unique factorisation into prime ideals. Now, a question that might actually be answered is "what happened after the late 1920s in commutative algebra to change this?" To which there is a fairly clear answer, implied by Goodwillie's comment: geometric concepts now mean more than those derived from algebraic number theory. "Dimension 1" seems more a propos or right-thinking than "dimension at most 1".