Tefillin on Chol HaMoed
In many communities, especially in Israel, the custom is not to put tefillin on during chol hamoed - the intermediate days of the holidays.
The reason we don’t put on tefillin on the holidays themselves, as well as on Shabbat, is that the tefillin are referred to in the Torah as an OT - a sign; but Shabbat and holidays are also considered a sign, so on these days we don’t display the “sign” of tefillin (Menachot 36b). What about chol hamoed?
Tosafot suggest that there are two distinct kinds of “signs” on the holidays. One kind of sign is refraining from labor, which is only on the holiday itself; the second kind is the special observances of the holidays, such as matza on Pesach and sitting in the sukkah on Sukkot, which exists also on chol hamoed.
Based on this idea, we could explain the difference of opinion regarding tefillin on chol hamoed based on which kind of sign the tefillin are. In one way, the tefillin are a sign of our inner dedication to HaShem, and our partial separation and elevation from worldly pursuits. After all, while wearing tefillin we have to avoid unclean places and acts (and thoughts). Here the appropriate parallel would be Yom Tov, and this approach would forbid tefillin only then.
In another way, the tefillin are an external sign, the prominent black boxes being a highly visible statement of our commitment to Torah. The prominent, external observances of chol hamoed reflect this aspect. This approach would add a prohibition on the intermediate days as well. (But not on Shavuot, when there is no external observance.)
The Beit Yosef (OC 31) cites the Zohar Chadash which also likens the two types of days to two aspects of tefillin. The Zohar Chadash refers to the holidays as the “tefillin” of HaShem: Yom Tov itself the head tefillin and the intermediate days the hand tefillin. On these days we are adorned by the tefillin of HaShem, and so it would be superfluous and even insolent to wear tefillin made by us (Zohar Chadash on Shir HaShirim, vol. IV p. 64 column d).
This distinction is closely related to that of the Tosafot. A common explanation of tefillin is that the head tefillin represent sanctity of thought, and those of the hand sanctity of deed. The Zohar likens Yom Tov, whose theme is the frame of mind of inner joy, to the head tefillin, and Chol HaMoed, with its special holiday observances, to the hand tefillin.
Since it is especially the hand tefillin which are called a “sign”, we can easily understand why the Zohar Chadash prohibits wearing tefillin on chol hamoed, and this is the custom of those communities who in general conduct themselves according to Zohar.
It is interesting to note that the Shulchan Arukh, who rules like the Zohar, also rules that no separate blessing is said on the head tefillin if it is put on together with those of the hand – both are exempted by the blessing said on the hand tefillin alone.
Based on the blessing, we would view the hand tefillin as the primary mitzva and the primary sign. The Rema, who rules that tefillin are put on during chol hamoed, holds that two berakhot are said on the head tefillin, and one of these (lehaniach) exempts the hand as well. Based on the blessing, we would view the head tefillin as the primary mitzva and the primary sign. Based on the distinction of the Zohar, the difference of approach regarding the blessings is parallel to that regarding tefillin on chol hamoed (Orach Chaim 25:5; 26:2; 31:2).