A Microsoft extension to the ANSI SQL language that includes procedural programming, local variables, and various support functions.
You have declare @DOW as nchar(7). That is, it's fixed length of seven characters. So if you do:
SET @DOW = '%3%'
--This returns nothing.
--SELECT * FROM c_Persons WHERE Workdays LIKE @DOW
You are search for strings that include the digit three followed by six spaces.
Change the datatype to nvarchar(7), and you should be fine.