If you are talking about taking a picture of an existing piece of art — "a framed picture" — the answer in most jurisdictions is probably no. Under the Berne Convention, which covers 172 countries, the creator of a work automatically has copyright over any artwork as soon as it is produced — and that includes creating a derivative work. Taking a photograph of another piece of art either creates a derivative work (if it is transformative), or just is that piece of work (if it isn't considered transformative). Either way, the copyright holder is legally in control.
This covers personal, non-commercial use as well. Now, you may be able to make a "fair use" case in some limited circumstances — but those circumstances are more limited than most people imagine.
If the copyright of the artwork is held by your host, I suggest... just asking. For the circumstances you describe, verbal permission is probably sufficient for all reasonable practical cases. If, on the other hand, the art is, for example, a photograph produced by a different artist, your host may not actually hold copyright and therefore not, from a legal standpoint, have the ability to give permission.
(Of course, from a practical sense, if your host doesn't mind and you're not using the result anywhere else, no one will ever be the wiser — but from strict legal reading, you're probably out of bounds.)
If, instead, you are talking about general photographs taken in someone's house, take a look at property-release for a number of questions discussing various circumstances. And, if it's a mix — a random shot which happens to contain a copyrighted work, know that this is a legal gray area where the legal resolution may not be immediately apparent.
Disclaimer: I'm not a lawyer. If you're in a situation where you need actual legal advice (like you took a photo at someone's house and are now in a dispute), please don't rely on random advice you find on the Internet.