The present perfect here indicates that it snowed last week and it is still snowing, or likely to snow, for the time being. The simple past would indicate that it was no longer snowing or no longer likely to snow at the time of the report - simple past is finished time and a specific time in the past.

Was the time phrase 'last week?' Or was it 'in the last week' ? If it was 'in the last week', this is a correct and natural use of the present perfect. This refers to the time period leading up to the present moment - similar to "up to now" or "so far". Please don't tell your students that we never use the present perfect with a specific time period - this isn't true at all! In fact, we often specify the time period with the present perfect. However, this has to be a time period which is either "open" and ongoing (such as 'this week') or which has just finished (such as "in the last week").