Its highly unlikely there will be snow on The Remarkables. We had a brief dusting this week post Ex Cyclone Gita but it's nearly gone already. Typically there is no snow locally in March unless we've had a freak cold snap.
You'll need to fly to land on a glacier in Mt Aspiring or Fiordland NP from Queenstown or Wanaka or take a flight from Franz Josef / Fox or Mt Cook to one of the nearby glaciers but again, unless we've had a cold snap, it won't be soft powdery snow, it'll be hard crunchy ice - sorry, it's just not really the time of year for snow.
Not knowing your whole itinerary I would say take the first opportunity you can for a glacier flight with a snow landing as all are weather dependent and if you wait for say Fox Glacier or Franz Josef you may not get up at all.
The only way you get to actually land on the glacier is if you take a helihike.All others are Glacier flights with a snow landing above the glacier.Edited: 24 February 2018, 18:14