The 32-year-old said apart from cold weather conditions, he and the other climbers were coping well.
The multi-national team had set up camp on the underside of the main deck and had enough supplies to last several days.
Smith said they also had the potential to re-supply if needed.
The Polar Pioneer was one of two drilling vessels heading towards the Arctic for Shell this year - according to Greenpeace - and is being transported on a 217 metre heavy-lift vessel called Blue Marlin.
The Greenpeace ship Esperanza followed the rig for 5000 nautical miles since it left Brunei Bay in Malaysia.
Tonight the Esperanza and its 35 person crew were stationed approximately one nautical mile from the rig.
Smith, who is based in South Auckland and has been climbing for 13 years, travels around New Zealand working as a contract climber.
He started volunteering with Greenpeace two years ago but said this was his first time climbing aboard a ship.
"I decided I had to take a stand because I don't think Shell have the right to go into the Arctic and cause the potential damage that may happen up there."
"I just hope that other people are inspired to stand up for what they believe in...stand up for what's morally right and have a voice."
Shell's drilling lease for the Chukchi Sea in the Alaskan Arctic was approved last week in the United States.
Both of its drilling vessels are crossing the Pacific and were expected to arrive in Seattle around the middle of April before heading to the Chukchi Sea.
Shell spokeswoman Kayla Macke confirmed protestors had "illegally boarded the Polar Pioneer, under contract to Shell, jeopardizing not only the safety of the crew on board, but the protestors themselves".
She added: "Shell has met with organizations and individuals who oppose energy exploration offshore Alaska. We respect their views and value the dialogue. We will not, however, condone the illegal tactics employed by Greenpeace. Nor will we allow these stunts to distract from preparations underway to execute a safe and responsible exploration program."