i can see some sense in splitting dates and times to be honest, although it isn't strictly necessary
think about outlook. you get a lot of entries on a calendar for a given date, which are then shown in time slots. So how do they do that? does the diary entry store the date and time in a single field - or does it store the date as an integer, and then store the time as a different field altogether. it may do either.
Times aren't really susceptible to a concise time picker, in a way that dates are - which makes dealing with times somewhat awkward.
It's a matter of taste, i suspect.
to take this a bit further - depending how you want to manipulate the times, may affect the way you need to store them. Im some apps, I just make the users enter a 2400 clock time, and force them to enter 4 characters such as 0800, and then store this as a text string
it's very easy to validate, and easy for users to input.