I went back to 07-08 season (the CoCoRaHS period, as I call it) and these are the longest streaks of at least a T of snow reported daily
12 days 12/21/12 - 01/01/13, 3.7 inches total
11 days 12/31/09 - 01/10/10, 4.3 inches total
10 days 02/27/13 - 03/08/13, 5.1 inches total
09 days 01/21/11 - 01/29/11, 2.5 inches total
09 days 01/16/14 - 01/24/14, 6.3 inches total
09 days 03/07/18 - 03/15/18, 3.0 inches total
08 days 12/02/10 - 12/09/10, 2.7 inches total
08 days 01/12/12 - 01/19/12, 0.4 inches total
the last is my favorite, ALL 'T' except one 0.4 recording.... so the 7 days is not as uncommon as I first thought... I am sure if I dug into the 'paper hard copies' from 80's 90's and 00's I would find more too. I need to spend a day or two on a vacation and get those into an Excel spreadsheet, it would be easier than what I am doing now, digging through years of paper records.