It is a rather humorous and ironic way of saying that gloomy winter's days are frequent in such cities. Nature bestows this kind of day with particular prodigality on such cities. "Bestow" is to give or grant something as a privilege or blessing; this is of course ironic, because what is being "bestowed" here is not at all desirable. "Prodigality" means generosity, liberality, lavishness. Again, the effect of this word is ironic, because it would normally apply to something desirable. "With particular prodigality" means "with special or outstanding generosity" or "in special or outstanding abundance". So nature grants such cities the [dubious] blessing of this kind of gloomy winter's day in particular abundance. Such days are particularly frequent in such cities, more so than elsewhere, it is implied.

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Note added at 44 mins (2013-11-30 09:20:07 GMT)
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As a statement about climate, this is presumably not literally true. It is a way of expressing the idea that small and backward states are gloomy and depressing places, precisely not favoured by nature. The seemingly habitual bad weather seems consistent with the nature of the place.