There's been some buzz in the pagan veiling community (I just have to pause to note how awesome that statement is. Pagan veiling community!) as to if one should cover their head during ritual or not. The consensus seems to be: yes, except for when you don't. Like veiling at other times, there is a whole spectrum of responses to this question. I can not speak for others here, nor would I attempt to. I do, however, wish to share some of what I have observed from the sidelines of this discussion and give my angle on the matter.
There seems to be a higher percentage of people who veil for religious observances (ie. whilst praying, giving offerings, etc.) than those who veil for magical working. The general arguments in favor of covering one's head for religious observances seem to fall along three lines. The first is that it is something that has historical precedent for one's practices. (Religio Romana seems to be the best documented case of this from what I can tell.) As there are many who are either influenced by reconstrutionist positions or active in reconstructionist pursuit of their faith, this argument really makes a lot of logical sense. Being a person who has a very eclectic background, I can find some examples (like in some branches of Filianism) where there is an established practice of doing this in my own roots.
The second general argument in favor of covering one's head for religious observances is to distinguish it from 'normal' time. It is, for some, the equivalent of putting on their Sunday best before going to pray. It is both a gesture of respect and a gesture that denotes the sacred as different from the 'mundane.' There really is a lot to be said for this position. It is one that is actually pretty common across religious lines (if you include all forms of special dress for worship) and veiling just seems to be another manifestation of this. I don't know if it makes prayer more effective beyond the fact that it helps the practitioner focus more intently on it. As I don't really engage in this practice, I can't say much about it beyond the fact that it happens, like the former argument.
The third general argument for veiling during religious observances is because it is observing a taboo. I set this apart from following established precedent because not all taboos have such origins. There are some who are called to cover when they engage in prayer and that calling comes from no higher then that of their deity of belief. This argument could, I suppose, supersede the others but I think that is just playing with semantics. (For the record, when I engage in formal worship activities for Dea, she has instructed me to have my head covered for some forms of worship and bared for others. As of right now, I am not able to speak much about this set of taboos beyond noting that they are present.)
The arguments against veiling during religious observances are myriad as well. Just as there is historical precedent for having one's head covered during worship, there is precedent for having one's head bared. There are those who are instructed to adhere to a taboo that requires them to be bareheaded at worship and others who do so for the sake of comfort and to distinguish from their daily practice of covering. In looking at both sides of this, I can only say that they all are legitimate positions and they should all be respected. Everyone's individual circumstances are going to be different and have different requirements and needs.