So, which is it? Certainly everyone in my Prowse circle spells with a 'W' but we also know there were alternate historical spellings, amongst them, Prouse.
Though I always assumed my grandmother's maiden name was spelled Prowse, as in Juliette Prowse, whom my mother adored, it wasn't until I ran a search with the filters loosened to include similar spellings (by the way, Price comes up often as well) that I found a 1911 census record for Annie Prouse that opened up the Prowse universe to me. More interesting is that the 1901 census, birth, and marriage records all use Prowse. Annie married in 1919, so any records after that were under her married name, Davison.
Along the way, I found other examples of Prouse instead of Prowse, mostly census records. However, when we get back to the common ancestor for most of us, Samuel's (1820-1886) grandfather, John (1756-1829), the records revert to Prouse. Why?
Enter, the history of the Alphabet. according to the website Day Translations, the use of double U's began in the middle ages under Charlemagne to denote a different pronunciation (more like a V) than a single U. However, the first mashing together in print of the two U's into a W came only a relatively short time ago, in 1700. This is not that many years before John Prouse was born and, well, some habits die hard. Wikipedia has a much more detailed explanation for those that wish to follow the yellow-brick linguistic road.
Of course, there is a flaw in the logic of this argument; the W, or OU for that matter, in Prowse is not pronounced like a V. Perhaps another explanation, again, based on the evolution of the alphabet to include the letter W, is that the OU combination in Prouse can be read and pronounced at least a few ways, while when replaced by a W, there is really only one way to pronounce the name.