ok, in my personal opinion you'll be fine with oem/"all season" tires when on regularly traveled roads/urban areas in the snow (which is what i assume you mean by "bad weather").
if you're in an area (like out in the country) that doesn't get plowed/traveled -alot-, then i would highly recommend getting some snow/severe snow rated tires. i personally like the bfg all-terrains, but really anything is going to be better than the bfg long trails (not sure what you have on yours though) that mine came with. in my research i've read that in general the "mud terrains" do worse in snow (due to the large blocks that just 'dig' into the snow) than the "all terrains" (not to be confused with "all-season" tires). however do some of your own research, as everyone has their own opinion
