If your birds live in an outdoor aviary, they can make their own d3 via a chemical reaction to sunlight. Birds living indoors don't get the full spectrum and ultraviolet light they need to produce d3 naturally. I like to use Calcivet or Breeding Aid. Both are great additives for any finches. Calcivet is mainly a calcium additive and Breeding Aid will contain the essential vitamins and fatty acids.
Species vary on how well they adapt to unfamiliar surroundings, and general flightiness.
Some species also do better in small flocks or colonies and others are more comfortable in single pair breeding cages or flights. A finch that is severely stressed may pluck it's feathers or other birds feathers, may be more aggressive, and may not eat well. Cold can be a problem in the winter months, and it is not only the cold but the over all dry air that compounds the problem. The muscles do not function and open properly when they are cold and dry. Note that each species of finch has it's own ideal size and weight.