Sometimes things are not as simple as one would imagine at first, and the beginning of the Chinese Astrological Year is a good example of it, there is no consensus on this among Chinese Astrology practitioners, some use the date of the beginning of the Tiger's Month (around February 4th), others the beginning of the Chinese new Year (also called the Spring Festival, when Chinese people do the famous party), and there are still those who use the winter solstice, usually December 22 or so.
This graph compares the 3 theories in an easy to understand way:
Basically what is not clear is the sign of people born between late December and mid-February, it is generally best to see both possibilities and the features of the two signs that could be, then according to what you know of that person and his/her way of being, see for yourself which option makes more sense.
This is why I implemented the ability to make calculations according to each of these three theories in the programs available on this website (Chinese Natal Chart and signs compatibility), thus it is easy to compare the results and see which one seems more plausible.
I also wrote this article where I do a more detailed review of this issue by analyzing some practical examples.
The truth is that the Chinese Horoscope, like so many things, is not as simple as it may seem at first, and the more you get in depth into it, the more you realize that there are more unknowns than certainties... but I think this somehow makes it also more fun and interesting! ^_^