Rabbi Chayim Pinchas Scheinberg is paraphrased (in The Radiance of Shabbos by Rabbi Simcha Bunim Cohen) as saying that, even if one will not cut into the second loaf, he should hold it unwrapped. However, Rabbi Cohen gives no reason for this rule. Sh'miras Shabas K'hilchasah, chapter 55, footnote 38, also says it should be unwrapped, citing Mishna B'rura [who is (eventually) quoting the Y'rushalmi].
Sh'miras Shabas K'hilchasah 55:12 says frozen bread is okay, citing B'tzel Hachochma (volume 3, 110:4) and Riv'vos Efrayim (volume 2, 115:2). (They allow it because one can extend his meal until the bread is edible; SSK notes, though, that he heard from Rabbi Sh'lomo Zalman Auerbach that it can't be used unless one plans to extend his meal that long, in which case the bread is "כרותח שצריכים להמתין עד שיצטנן" [which I don't understand].)