Bnei Yisrael’s relationship with HaShem is often described as a marriage; HaShem is the groom and Bnei Yisrael are His bride. See Shir HaShirim for an extended example. The Prophets frequently compared the relationship between Hashem and Israel to the relationship between bridegroom and bride and/or the relationship between husband and wife. For example, regarding the reconciliation of Israel with Hashem, it is written, “As the bridegroom rejoices over the bride, so shall your God rejoice over you” (Isaiah 63:5). And it is also written regarding this reconcilation, “And it shall be on that day, spoke Hashem, that you will call Me, ‘my Husband’ ”(Hosea 2:18). There are many other examples that can be found, but here's my question, although it might be a little far fetched..
If Bnei Yisrael is compared to a bride, and it is the custom for brides to cover their heads, could the headcovering (for woman, when praying for example) be a symbolic sign of being a bride of HaShem (i.e. being a sign of commitment to HaShem; commitment to a covenent/Torah keeping lifestyle)?
Are there any commentaries regarding to this?