I'm not sure where or when this "rule" started, but its day has passed. I can assure you, it's just a historical version of fashion etiquette, and not an actual law. I know this for a fact, because I've done it, and I have lived to tell the tale.
Having said that, it is definitely more difficult to find white shoes during cold months. People tend to gravitate towards colors that seem "warmer," like browns, oranges and reds, thus the majority of people may prefer not wearing white during cooler months. But doing so is not poor etiquette or distasteful -- it's just a matter of preference.
The fact is, certain colors may call to mind specific seasons (rust in fall, yellow in summer, light blue in spring), but shoes don't actually look better at certain times of the year. A fab pair of pink shoes will look just as fab in Autumn as they will in Spring -- though you might have difficulty finding seasonal clothes to wear with them. This is because fashion tends to draw from colors that are found in nature at any given time of the year.
Ironically, an abundance of white is found in nature during the winter months, so it makes the concept of "no white shoes after Labor Day" even more silly.
White and winter go together as well as, say, snow and winter.
Personally, I love white boots, white hats, white scarves and white coats -- I say, the more white in winter, the better. Wear it proudly.
Now wearing summer shoe styles in the dead of winter ... well, that's just wrong.