Mr Owen advised drivers to take care.
"Our transport operations centre is open 24 hours a day so we'll be keeping a very close eye on conditions and managing any incidents on the road in partnership with our contractors and NZ Police," he said.
Drivers who had pulled up at the pass in the morning to view the scene began departing as the snow increased, with the road closing again after 11am.
Elena Lynch, from Featherston, stopped for a snowball fight with a friend.
They were heading to Petone, but were worried the hill would be closed. They opted to turn back.
Readers sent messages to Times-Age on Facebook in the afternoon, describing their journey.
Andy Rigg posted at 3.30pm, "we are just driving over to Wgtn. No problem getting through ... but had some hail & snow. Snow banked up on side but road ok. The lads are at the top with their graders ready & waiting!"
At 3pm Marquerite Vierstraete posted, "just got back over from Wellington, beautiful views, slippery though on the road."
NZTA Central Region media manager Anthony Frith said when snow is coming it has contractors ready to respond.
"They are mobilised, ready to charge in and help people and keep them safe."
Met Service warns snow showers are expected to affect the road till later this morning.