Yeah usually, but it's hard to do so unless it's a 3 day weekend. Depending on your class schedule, on a Blue Friday you might be in class until 1523, so that + the drive to the airport are usually limiting factors. The accountability/privilege/pass system changes almost every year, as well, so the time you need to be back Sunday could be as early as 1900, which limits the practicality as well. Silver weekends are pretty much never practical, since you typically aren't released until sometime on Saturday.
Cadets going home/elsewhere during 3 day weekends that are also blue (Columbus, MLK, etc) is a very common occurrence. There's just some paperwork you need to fill out and have approved by your squadron leadership in advance any time you're trying to leave a 150 mile radius of the base.
Funerals/other reasons for emergency leave are kind of the other big exception here, but that's a completely separate process.