Most ski areas have lockers (aka baskets in area not accessible to the public with counter for access, you can access basket as much as you like during hte day) that you can leave gear in for a few dollars for the day, and you can
I would definitely wear your shoes and put them in a locker. Some people leave their gear under tables in the cafe, including backpacks, but don't leave anything you don't want to lose.
As for a rental car, it does give you the most freedom, but I would only get a car if you are comfortable driving on mountain roads. The roads to the ski area are shingle/gravel/metal, and climb over 1,000 metres up from the valley floors to get to the snow line, and there are not a lot of safety barriers, and trees (ie. a big drop). You may have to fit chains, more frequently if 2WD. 4WD must always carry chains so they can be fitted if the roads become icy (much less frequently). If you rent, get a 4WD, makes the experience much nicer. I probably make it sound worse than it is, but many people from overseas find the ski areas roas here quite daunting. If you are used to driving in snowy conditions, and have a head for heights, you will be fine.
If you have a car then you can move on if the conditions are nto good. When the nor'wester starts to blow, Mt Hutt can be shut for serveal days at a time (hence the nickname Mt Shutt), if you have a car you could head south to Wanaka where the nor-wester does not affect them so much. The snow conditions between the Queenstown/Wanaka region, and Canterbury (Mt Hutt etc) can vary, some years Canterbury is better than Queenstown/Wanaka, other years it is better. They might look close on the map, but they get impacted by different snow storms.
The Methevn/Mt Hutt experience might be alright for a couple of days, but if you are coming all this way I would suggest heading south to Wanaka/Queenstown, a lot more going on. If you don't like groomed slops, you should check out at least one club field while you are here, they are all in Canterbury. I'd suggest Craigieburn (www.craigieburn.co.nz
). You can stay on the mountain (need a sleeping bag and towel) , and is a completely different ski experience to anything you'd have overseas, they are the only places you can stay on the mountains - meals included. They use nut cracker rope tows and there are no groomers, so it can be very tiring. I'd suggest trying it at the end of your holiday so you don't wear yourself out for the rest, but then if you really like it you may not want to go elsewhere.
There are some ski deals about at the moment with vehicleswww.skiwi.co.nzwww.skiexpress.co.nz