This should do what you are looking for

DECLARE @datetest TABLE (CaseID INT, MTDThresholdDate date, YTDThresholdDate date);

INSERT INTO @datetest (CaseID, MTDThresholdDate, YTDThresholdDate)

VALUES (1, NULL, NULL)

, (2, NULL, '2016-05-15')

, (3, '2016-06-15', NULL)

, (4, '2016-05-05', '2016-06-15')

, (5, '2016-06-05', '2016-05-15')

DECLARE @MaxDate DATE = '2999-12-31';

SELECT MT.CaseID, MinDate = NULLIF(MA.MinDate, @MaxDate), MinDateCol = MA.ColName

FROM @datetest AS MT

CROSS APPLY (

SELECT TOP(1) VA.ColName, VA.DateCol

FROM (VALUES('MTDThresholdDate', ISNULL(MT.MTDThresholdDate, @MaxDate)),('YTDThresholdDate', ISNULL(MT.YTDThresholdDate, @MaxDate))) AS VA(ColName, DateCol)

ORDER BY VA.DateCol

) AS MA(ColName, MinDate);

EDIT: Added code tags