Bodily hair is considered "dead skin" and incompatible with spiritual practice / rituals in the Vedas.
mṛtām eva tvacam amedhyām apahatya yajñiyo bhūtvā medham upaiti
(Taittiriya Samhita 126.96.36.199)
Thus practitioners of Vedic yajnas would periodically shave bodily hair. Even though the practice of daily Vedic yajans has almost become extinct, the spirit behind the practice is still being followed as other forms of ritual worship are considered equivalent to yajnas.
The Dharma Shastras prescribe the shaving of some kinds of body hair (head, face for brahmacharis and grihastas; armpits, chest, back, genitals and wrists for grihastas) and finger/toe nails.
The practices of having the hair on the head trimmed, or shaving facial hair alone are quite modern and unsanctioned by the Dharma Shastras. Vapana is to be done in entirety on the prescribed days (because otherwise it would be meaningless to hold on to some impurities instead of discarding it off completely).
Prolonged periods of non shaving (called dīkṣā) are also prescribed for various situations, eg.
- For the participant in a long yajna or vrata for the duration of the yajna (Shatapatha Brahmana, various Srauta Sutras),
- For the husband of a pregnant wife during the pregnancy period (Apastamba Grihya Sutra),
- For the cremation-performer for the period of the first year (Smritimuktaphalam, Aashaucha Khanda).
The allowed days for Vapana can be found various Dharmasastra texts such as in Vaidyanatha Dikshita's SmritimuktAphalam and the Dharma Sindhu of Kasinath Upadhyay (in the tithi-vrAtya-nirNayas of the first section).
A summary of the Smritimuktaphalam in the Tamil language titled "Dharma Sastra Surukkam" edited by Krishnamurthi Sastrigal lists Monday, Wednesday and Thursday as the suitable days of the week for Vapana in conjunction with the Tithis - 2,3,5,7,10,13
Note that all of the above is only for the Brahmana varna.
Members of other varna have other rules. Members of the fourth varNa who work as cooks for example are required to daily trim their nails, and hair on face, head and body.
adhikam ahar ahaḥ keśa śmaśru loma nakha vāpanam (Apastamba Dharma Sutra 2.2.3)