Even with the cover (because it has vent holes), I can't really avoid the problem of snow getting into the radiator fans. And I can't fully clean them by hand, either. Fortunately they don't generally run in the winter (but can, especially with heat & A/C while sitting still).
Also have to be careful about the way you clean it. The curves take more time to clean around, and you want to clean in the right direction so as to, for example, not shove snow in the air ducts