Parsing and formatting a time two ways (perfectionistic approach)
In the 2nd version, the if acts as a guard: it prevents invalid states to get through it. Many people prefer it this way, for example in this related post: 
Should I return from a function early or use an if statement?

Which way you choose, is a matter of taste. There's nothing wrong with either one.

If you do go with the 2nd one, it can be improved a little bit:

public override void OnEventTimeChanged()
{   
    TimeSpan eventTime;
    if (!TimeSpan.TryParse(EventTime, out eventTime))
    {
        return;
    }

    DateTime eventDateWithTime = EventDate.Date + eventTime;
    CultureInfo cultureInfo = Thread.CurrentThread.CurrentUICulture;    
    string eventTimeString = String.Format(cultureInfo, "{0:HH:mm}", eventDateWithTime);

    EndTime = eventTimeString;
    EndDate = eventDateWithTime;
}


That is:


cultureInfo is not needed in the if, so declare and initialize it later. Even more precisely, declare and initialize it right before you really need it.
It's recommended to use braces with if statements always, even if only one line will go inside the block. Remember this bug: https://www.imperialviolet.org/2014/02/22/applebug.html