Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Milwaukee to Wellington as you normally would.
In terms of precipitation, rainfall in Wellington ranges from 2.8 - 5.1 inches per month. July is typically the wettest month, when rainfall can reach 5.1 in. January is typically the driest time to visit Wellington when rainfall is around 2.8 in.
If weather is an important factor for your trip to Wellington, use this chart to help with planning. For those seeking warmer temperatures, January is the ideal time of year to visit, when temperatures reach an average of 62.6 F. Travelers looking to avoid the cold should look outside of July, when temperatures are typically at their lowest (around 48.2 F).