It's fairly common to only want a date out of a datetime - you should be able to Google for the specifics of your RDBMS (since you don't mention it). The important bit is to make your query SARGable by transforming today's date1 - not the order date.
For MSSQL, something like
SELECT DISTINCT CustomerID
FROM TableName
--I assume you want midnight orders as well - so use >=
Where OrderDate >= DATEADD(dd, 0, DATEDIFF(dd, 0, GETDATE()))
would work by taking number of days today is from Date 0 (DATEDIFF(dd, 0, GETDATE())
) and adding them back to Date 0 (DATEADD(dd, 0, x)
). That's T-SQL specific, though.
1 If you were searching for an arbitrary date, you'd still transform both arguments:
SELECT DISTINCT CustomerID
FROM TableName
Where
OrderDate >= DATEADD(dd, 0, DATEDIFF(dd, 0, GETDATE()))
--You *do not* want midnight of the next day, as it would duplicate orders
AND OrderDate < DATEADD(dd, 0, DATEDIFF(dd, 0, GETDATE()) + 1)