Officers would also check cars to see if all vehicle occupants, including children, were safely buckled in.
"While it's inevitable that we all make mistakes, we don't want to see anyone lose their life or be left permanently scarred because of it - and there's simple things that we can all do to help make sure that doesn't happen."
Mr Greally said police would enforce a reduced speed threshold so anybody going more than 4km/h above the speed limit could bank on getting a ticket.
Police also pledged to punish people who might be tempted to use their cellphones while driving.
Authorities have said black ice on roads was another danger.
"With the recent wintry cold snap we urge everyone to drive to the conditions, which means reducing your speed and extending your following distance, particularly in the wet and where there is reduced visibility," Mr Greally added.
"Traffic congestion around the main centres is also likely to be worse as people head away for the break, so think about timing your journey to avoid those peak times, and be prepared to be patient if there are delays," he said.
Fatigue was another potential killer, he said, so drivers should take plenty of rest breaks.
The official Queen's Birthday weekend runs until 6am on Tuesday.
The New Zealand Transport Agency (NZTA) suggested people check for good tyre tread depth, and ensure lights, brakes, cooling systems, demisters, wiper blades and batteries were working.
"Ensure your spare tyre and tools are in good condition too," the agency added.
Clean windscreens helped minimise the impact of sunstrike, so NZTA advised drivers to keep a cloth and window cleaner in the car.
The agency said people should not leave until they could see clearly out both windscreens, all windows, and rear and side mirrors.
"Allow a few extra minutes for your demister to do its job."
With later sunrises, earlier sunsets, and often cloudier skies, winter also created visibility issues so the NZTA said drivers should consider keeping lights on at all times.
The NZTA also said motorists should have a plan in case of breakdowns, and carry warm clothes, sturdy shoes, food, a torch and a first aid kit.
Meanwhile, partial closures on Auckland's Northwestern Motorway could impact some motorists.
The agency said the motorway will be shut both ways between Te Atatu and Lincoln roads from 8pm Saturday to 8am Sunday to connect some new sections of a bridge.
"We are encouraging people to travel outside of the closure times if possible, or consider alternative routes such as State Highway 1 and the Harbour Bridge," NZTA Auckland and Northland highway manager Brett Gliddon said.
A detour between Te Atatu and Lincoln roads would be available for drivers but the northwestern cycleway would stay open.
NZTA advised drivers across the country to make sure their cars were "winter-ready" before heading off.
