This is a question about writing mechanics and punctuation. The traditional rule is that introductory adverbials like During church and During the long arctic winter should always be set off by a comma. Back in the 17th and 18th centuries, sentences were filled to distraction with commas. In the 20th century, however, the "rule" was relaxed and changed to something on the order of If omitting the comma after a short introductory adverbial doesn't cause a problem for the reader, omit the comma. "Short" meant 3 words or 5 words (maximum), depending upon the style manual.
In the 21st century, writers of all stripes have become comma-ists ("racist against commas" to use the trendy fuzzy jargon of the 1980s) and don't like to use commas even when they're necessary.
My assessment is that neither of your sentences requires a comma because neither sentence without the comma leads the reader down a garden path to misunderstanding or forces the reader to reread the sentence to be able to understand it. The only reason to include the comma is pedantic adherence to an outmoded rule (which is my problem: I don't hate commas) or to tell the reader to pause slightly. The comma will affect the rhythm and, therefore, the flow of the sentence when read silently and aloud.
Whether a comma should appear has nothing to do with whether the word "during" appears at the beginning of a sentence.