My Glossary of Computing Terms: An Introduction (pub BCS, 1984) says
Field is a predetermined section of a record
which covers forms as well.
OED shows the origin is surprisingly early:
19. Computing. Any one of a number of places where a user is expected to enter a single item of a particular type of data; an item of such data; esp. one in a database record. Cf. data field n. at data n.
Originally a group of columns on a punched card.
1903 Jrnl. Polit. Econ. 11 372 The fields are to be punched in the regular order by touching the keys indicated from left to right.
Data field was apparently first mentioned in a patent:
data field n. a section of a record, esp. in a database, in which an item of data is entered; each of the particular types of data held in a database.
1929 Brit. Patent 302,314 9/9 A previous inventory perforated strip P1, the separate data fields of which give, inter alia, the following data [etc.].
It's a fairly small step to extend other earlier uses to reach the above meanings:
10. a. An enclosed or marked-out area [for playing sport]
or even
II. An area of operation or observation.
12. a. An area or sphere of action, enquiry, or interest; a (wider or narrower) range of opportunities, or of objects, for activity or consideration; a theme, a subject. Freq. with of.
b. As a mass noun: scope, opportunity; extent of material for some specified action or operation. Freq. with for.
c. A particular branch of study or area of expertise or competence; a subject. Also more fully field of study.
You pose what I take to be two questions:
(1) Why is 'head hair' two words instead of one (especially given other words like bedroom)?
We all know what a car radio, a toaster oven, a graveyard shift and a spring chicken are; I don't think we'd benefit from making them a single word, even if other languages might do so -- indeed French and German have 'autoradio' instead.
'Word count' is really about language-specific word derivation practices, practices that might be constrained by grammar or just by custom.
The more interesting question you pose is
(2) Why is there no separate lexeme for head hair?
Well, as others mentioned, there are rare words like 'chevelure' and 'coif' that may fit the bill; on the other hand, they might be better viewed as foreign words. In any case even without them I think we need to remember that vocabulary does not develop merely as a result of 'need': there is a lot of randomness in language (one might draw an analogy to 'genetic drift' in the theory of evolution, which results in random elimination of some genes in a population, merely as a result of chance (http://evolution.berkeley.edu/evosite/evo101/IIIDGeneticdrift.shtml)).
I personally think that English has a lot of vocabulary that is not 'needed' by any objective, non-sentimental criteria, since other languages seem to make do with paraphrase in the same situation (and likewise for other languages). Vocabulary seems to develop by random acts of creativity that are not especially 'useful' (slang is a perfect example, which lives and dies on sociological grounds, rather than on 'being unable to express oneself otherwise', although I accept the distinction between the two is not quite that clear-cut).
PS The word for 'gloves' in German is 'Handschuhe', or 'hand shoes'. No separate lexeme.
In brief, I think it is mostly because of chance that there is no separate lexeme for head hair.
Good evidence against this view would be evidence that, for example, discussion of head hair was taboo among prior English speakers (for example, because it invited the wrath of God. Many religions do still have hair taboos). A similar phenomenon is believed to have occurred for 'bear', which in many languages is derived from a circumlocution. In Croatian the word for 'bear' is literally 'honey-eater.' Even English's 'bear' is derived from 'brown.' The reasons are thought to have to do with warding off bad luck by avoiding a direct, separate name. See http://www.cloudline.org/LinguisticArchaeology.html.
But I know of no evidence for such a theory as regards head hair, nor even for the simpler theory that English speakers thought of head hair in a different way (a culture-determines-vocabulary type argument).
Best Answer
The OED says that this was a common sound change first attested in writing around the year 1400 (but doubtless preceding that in speaking) that also occurred in many other similar words of this general form, including also hither and feather, as well as the kinship terms father, mother, brother. All those words in the OED reference a common note in their history of the word father in which these three sentences about the matter can be read:
With respect to interim forms and geographic variance, the written evidence shows that just exactly when and where this happened across Britain varied significantly. Indeed some words which in some writings for a long while enjoyed this same d > th change nonetheless eventually settled on the d version instead of on the th version long used with them. The noun rudder is one of these which commonly enjoyed th for a long while before now being spelt with d.