Way back in the beginning of Java (i.e., Java 1.0), the date/time api largely (solely?) consisted of the Date class. The Java folks were aware that it lacked robustness, so they added the Calendar class in Java 1.1 and tried to change the Date class into a value object by deprecating most of it. Unfortunately, the Calendar class itself wasn't very well thought-out (see here) and we're stuck with what many consider to be a monstrosity.
Bringing us up to today, GWT supports Date because, well... how can you live without dates?, but doesn't support Calendar/GregorianCalendar/TimeZone because it's so ugly and surely there has to be a better answer. Sadly, no one's thought of it in over 3 years as Calendar support was requested way back in January of 2007 and marked as planned by April 2008.
In short, go ahead and use the the deprecated Date methods in your GWT code, if that will work for what you need to do.