Weight is actually a good thing in the snow. Too light of a vehicle and it's hard to get any traction without something like tracks.
The struggling in the snow is most likely an issue of tires. If someone put some all terrain or ideally snow tires, I'm sure it'd do significantly better.
But it can't afford to run less efficient tires because it has too much air resistance and the range would suffer. There's a reason why other Teslas have no flat panels or straight lines.
I don't disagree with that at all, it's a dumb vehicle no matter how you slice it and this debacle only furthers the proof. If it needs low rolling resistance, highway tires, then it's just a street queen for elon fanboys.
Weight alone doesn't help. It matters where the weight is. On a rear wheel drive vehicle it absolutely does help with traction and handling if you add more weight on the rear axle. People have been hauling sandbags on their truck beds/trunks in the winter for ages for a good reason.