This is a question I am asked on occasion and my usual answer is ‘It depends’.
I would say, though, that winter is a definite no-no, simply because of the unpredictability of the weather. If we could guarantee a mild, frost and snow free winter, then that would be great but, of course, we can’t, and it is not worth taking the risk.
The alternatives then are either the spring and summer or the autumn and both have factors in their favour.
If you are looking for a quick build then spring and summer are definitely the seasons to favour. You will benefit from the dry weather and the long daylight hours will really let you crack on.
However, if cost is a consideration you may be better off waiting until the autumn. The reason is that costs of materials often fall at this time of year, precisely because fewer new builds are taking place.
Providing you can get the main construction completed before any bad weather, then I would recommend starting building in September or October.