The airframe can do +4G to -2G. Based on that and the abuse the gear takes during landing, I'd say it can take at least its own weight in snow and ice, probably more.
The wing area is about 160 sq ft, add another 100 max for the fuselage/tail.
2200 lbs of snow would add up to about 8 lbs/sq ft, which is mid-way between light and heavy for 1 ft of snow thikness. In practice, you won't have perfect height at the edges, so it'll probably take 1 ft of heavy snow to add up to that weight.
So, I'd guesstimate between a foot and two of snow before you need to start thinking about it. Which lines up well with pictures of aircraft parked outside and covered in snow that I've seen.