You should try printing your commandcommands when they yield errors. If you issued this instead of executing it:
Which isn't even a valid BETWEENBETWEEN
operation, even if it could translate those to dates.
As for the overall requirement, here is how I would do it (I confess I did not even look at the SO question):
DECLARE @b DATE = '2012-07-01', @e DATE = '2014-01-25',
@sql NVARCHAR(MAX) = N'';
SELECT @sql += N'
DELETE ' + QUOTENAME(s.name)
+ '.' + QUOTENAME(t.name) + '
WHERE ' + QUOTENAME(c.name) + ' >= @b
AND ' + QUOTENAME(c.name) + ' < DATEADD(DAY, 1, @e);'
FROM sys.tables AS t
INNER JOIN sys.schemas AS s
ON t.[schema_id] = s.[schema_id]
INNER JOIN sys.columns AS c
ON t.[object_id] = c.[object_id]
WHERE c.system_type_id IN (40,42,43,58,61);
-- or just = 40 if you're only interested in DATE columns
PRINT @sql;
-- EXEC sp_executesql @sql, N'@b DATE, @e DATE', @b, @e;