Update only Date portion of DateTime

 UPDATE table1 
 SET columnDatetime = '10/5/2012' + ' ' + CONVERT(varchar(12), CONVERT(time, columnDatetime))
 WHERE CONVERT(date, columnDatetime) = '10/4/2012'

Just use varchar and modify what you want in it without touch the time. In this example I use CONVERT(varchar(12), columnDatetime) to get a string with length of 12 characteres assuming a case of time with a format for example like "20:10:15.250".

CREATE TABLE dbo.MyTable(
    ID INT IDENTITY(1,1) PRIMARY KEY,
    DTColumn DATETIME NOT NULL
);
GO
INSERT dbo.MyTable(DTColumn) VALUES 
('20120410 08:03:00.000'),
('20010101 01:01:01.000');

BEGIN TRANSACTION;
    UPDATE  dbo.MyTable
    -- Style 126 / ISO8601 = yyyy-mm-ddThh:mi:ss.mmm        
    SET     DTColumn = STUFF(CONVERT(VARCHAR(50),DTColumn,126) ,1, 10, '2012-05-10') 
    -- Uncomment this line to see the old and new values
    -- OUTPUT   deleted.DTColumn AS OldValue, inserted.DTColumn AS NewValue
    WHERE   CONVERT(DATE,DTColumn)='2012-04-10' 

    SELECT * FROM dbo.MyTable;
ROLLBACK;
-- COMMIT

Results:

OldValue                NewValue
----------------------- -----------------------
2012-04-10 08:03:00.000 2012-05-10 08:03:00.000

ID          DTColumn
----------- -----------------------
1           2012-05-10 08:03:00.000
2           2001-01-01 01:01:01.000

UPDATE
    tableX
SET
    columnX = DATEADD( day, DATEDIFF( day, columnX, '20120510' ), columnX ) 
WHERE
    (conditionX) ;

UPDATE YourTable
SET YourColumn = DATEADD(MONTH,1,YourColumn) 
WHERE YourColumn = '20120410 08:03:00'

I assumed that you posted your date on DD/MM/YYYY format. If it was MM/DD/YYYY you should use DATEADD(DAY,1,YourColumn) instead.