You can
absolutely get heavy snow in late October in the mountains around Jasper.
Let me put it this way: it is very common (more often than not) to have snow in Calgary (3000 ft elevation) at Halloween. Mountainous areas have
already had snow (ie. Crowsnest Pass) in mid-SEPTEMBER this year!
I would discourage you from planning o taking the NSX. If you've got your heart set on it, make sure you're wearing either snow tires or perhaps good all-season tires with an open tread block pattern and good for maintaining traction at temperatures between -20C and 0C (-5F to 32F). Otherwise your drive may be a little more exciting than you wish!
That said, take a different vehicle and enjoy the drive. It's a beatiful area.