I think everything depends on the individual credit card company.

I travel overseas a great deal both for work and for pleasure. I generally use my ex-Charles Schwab Visa card because they don't charge a foreign-transaction fee and I still get a 2% rebate. I don't think I've ever given them advance notice of my trips in the four-five years I've had the card, and I've never once had a transaction declined. I also go to a wide range of countries - developed places like Canada and Europe but also Bolivia, Peru, Brazil, etc. In the past, when using other cards (Cap One, HSBC, etc.) I've also had no problems that I can recall, and again I almost never gave advance notice.

That said, I have heard stories (like some of the ones in the comments) about people having their cards frozen with no warning when traveling overseas. Weirdly, while I've had no problems overseas, I have had problems with cards that I've used in the US - my old Citi Premier Pass card went through a phase where they suddenly kept denying my weekly DC subway pass purchase, despite the fact that I'd made the same transaction every week at the same train station for about two years. That took multiple calls to sort out, too.

As to what to do for an extended move, I'd notify your card company to make sure they have the address on file. When I lived in the UK for six months years ago (back in the days before Internet commerce) and in Canada more recently, my cards had no trouble sending me paper bills by international mail. If your card is going to expire soon, perhaps you can get them to just issue you a new card before you go.

If you'll be in Hungary for an extended period, though, I'd recommend just getting a credit card from a Hungarian bank as soon as you can. Your school may be able to help you with the paperwork. At least get a local bank account with a debit card, for obvious reasons.