Is a head covering needed any time a prayer is said (i.e. before dinner, around the house, baseball game, Bible class, etc.) or just during a worship service?
"But every woman who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved." (I Corinthians 11:5).
Notice that a covering was required by a woman for both prayers and prophecy. The wording is such that the woman is participating in these acts. However, during worship a woman is to remain silent. "Let your women keep silent in the churches, for they are not permitted to speak; but they are to be submissive, as the law also says. And if they want to learn something, let them ask their own husbands at home; for it is shameful for women to speak in church" (I Corinthians 14:34-35). While a person may pray quietly to God, prophecy required the prophet to speak out. But a woman isn't allowed to do that during worship services. In addition, the proofs Paul offers for this rule are not one based solely on the worship service. Therefore we conclude that that I Corinthians 11:1-16 is not limited solely to the worship service.