Is it just common sense that tells you the sentence is "There is rarely snow in the morning." rather than "There is rarely morning in snow."? Or is there some underlying grammar sorting out the relationship of snow to is?
To be honest, after a cold night, there's a higher probability for snow in the morning than in the evening.
Instead of "there is rarely snow in the morning", can't it translate into "it rarely snows in the morning"? Sounds more natural in English.
Like mizinamo said above, those are two different things in English as well. The first means "there is snow (even though it hasn't snowed in a week)", the second "it snows (finally, I was afraid we wouldn't have a white Christmas).