Comment by proberts
Yes. I still think that those with student or work visas or green cards should travel internationally. It's just a question of being smart and carrying the right documents. The right documents will vary depending on the status so I can't give a list but I'd recommend having a brief consultation with an attorney. Many like myself won't charge for a 15-minute consultation, which is all that this should take.
What would a green card holder need to carry other than their passport and greencard?