January in Conwy is the rainiest and the coldest month of the year. In January, the weather in Conwy is typically cold. Average daily high temperature in January is about 6 degrees above zero. On average, Conwy has 27 rainy, 3 sunny, and 1 partly cloudy day in January. The rains are usually heavy. January as well as February, March, April, and May is considered the most uncomfortable time to visit Conwy.