Taiwan will have the same week long holiday as the mainland, officially starting on the 18th. The biggest days are the first two: the 18th is new year's eve and the 19th is the first day of the new year. Things will be very busy. People come home from afar to be with their families during the holiday, so the population density goes up significantly.
Whether it will be frustrating depends on you, but difficult is a real possibility. Here are some important things to know:
- Shops, hotels and restaurants will be open - the cities don't shut down; this is peak travel season - but prices and hours may fluctuate significantly from the norm. For example, a small family run shop might close for the entire holiday, while a fancy banquet restaurant extends hours late into the night to attract partiers. There may be special events or sales, or management might raise prices. Anything that's open will be packed.
- Offices, banks, factories and the like will be closed. If the purpose of your trip is business, this is the wrong time to go.
- Leisure or tourist centric locations will generally be open (new year's eve and day likely excepted), but will be very busy, because a lot of people are off work and go out to celebrate with their families.
- Transportation services will remain open, but will be quite busy. Taiwan schedules extra trains during the holiday to ameliorate the high loads, but expect to feel like a sardine. Ticket prices are marked up a lot on account of high demand. Don't be surprised if they're sold out, even if you're trying to book a week or more in advance.
- If you don't have a hotel booked already, it will be nigh impossible to get one at this point, and very expensive if you do.
- There's a relative lull in travelling during the middle of the holiday. Relative to the start and end, that is; it's still much busier than the rest of the year.
However, this is a wonderful time to experience the local culture. It simply does not get more festive than the lunar new year celebration. You will not be hurting for excellent things to see, do and eat.