Try:
DECLARE @StartDate DATETIME, @EndDate DATETIME
SET @StartDate = '2013-10-22'
SET @EndDate = '2013-10-22'
SELECT FullName, DATEPART(MONTH, DateOfBirth) AS MONTH, DATEPART(DAY, DateOfBirth) AS DAY, CONVERT(VARCHAR(10), DateOfBirth, 111) AS DateOfBirth
FROM Customers
WHERE DATEADD(YEAR, DATEDIFF(YEAR, DateOfBirth, @StartDate), DateOfBirth) BETWEEN @StartDate AND @EndDate
OR DATEADD(YEAR, DATEDIFF(YEAR, DateOfBirth, @EndDate), DateOfBirth) BETWEEN @StartDate AND @EndDate
ORDER BY CASE WHEN DATEADD(YEAR, DATEDIFF(YEAR, DateOfBirth, @StartDate), DateOfBirth) BETWEEN @StartDate AND @EndDate THEN 1 ELSE 2 END,
DATEPART(MONTH, DateOfBirth), DATEPART(DAY, DateOfBirth)
Assuming your table name is "Customers" and the column name for DOB is "DateOfBirth"(I am assuming it to be of type DateTime). The same query can also be used to find DOB's within a date range.