I suppose a year number to be a proper noun, naming a unique year. Therefore, when written as text, it should be spelled with initial capital letters. But there does not seem to be general agreement about this.
Few authorities offer a rule at all, probably because year numbers are more commonly written as Arabic numerals. One source treats a year number as a common noun, like any number. A second agrees but says some authors consider a year number to be a pronoun when not preceded by the words "the year". A third says a year number names a unique year and must be treated as a proper noun, citing The Winston Grammar Program by Paul E. Erwin.
On wedding invitations, etiquette authorities agree, the year is traditionally written as text. It is for this reason, I suppose, that some authorities think to address capitalization of the year. However, there is no consensus. It is more common to see the advice to capitalize the first word of the year (only). Most Google search results for [ capitalize year wedding etiquette ] give this advice. On the other hand, that paragon of etiquette virtue, Emily Post, specifically prohibits it, saying only the names of weeks and months are to be capitalized.
In short, I can find support for three different capitalization rules for year numbers:
- no capitalization (written number rule), e.g.: "the year thirteen sixty-one"
- capitalize first initial letter (wedding invitation rule), e.g.: "the year Thirteen sixty-one"
- capitalize all initial letters (proper noun rule), e.g.: "the year Thirteen Sixty-one"
How should the year be capitalized?