The Winter Borough is a special District that can only be built once per city, and production can only be applied towards completing it during Winter. If the Winter Borough is not completed before the end of Winter, its production in the queue will be blocked, but not undone, so it is best to place it at the bottom of the queue until the next Winter and finish construction on it then.
The Broken Lords do not benefit from the Food effects of the Winter Borough.
Those who save in summer, profit in winter. Wise words, and in this case put to the test by preparing buildings, supplies, streets, and citizens for the worst of times.
A very important trait of the Winter Borough to note is that the bonus it provides to Food, Industry, and Dust applies to every City Tile in the City it's built in, which can provide a massive production boost to large cities in Winter. This construction in a city governed by a Hero with the Cold Operator skill (which grants immunity to all negative effects from Winter), can result in a City that operates more effectively in Winter, especially when coupled with other winter-specific bonuses such as Ice Works. This can be a huge benefit in the late game, when Winters become longer and have varied harsh penalties.