Is it permitted to smoke on Rosh Hashanah?
Although there are some who permit the practice, many rule that today it is forbidden to smoke on Rosh Hashanah (and on Yom Tov generally), and therefore the practice should be avoided.
Several poskim of previous generations (before health concerns became well known) discuss the question of smoking on Yom Tov.
The Torah (Shemot 12:16) permits kindling a fire on Yom Tov, but it remains forbidden (see Biur Halacha 502:1 s.v. Ein) to create a new fire on Yom Tov, which is why we light something on Yom Tov by transferring from a preexisting flame.
Yet, it is forbidden to burn incense on Yom Tov (Beitza 22b and Shulchan Aruch Orach Chaim 511:4), the reason being that burning which is not “shaveh le-chol nefesh” — something that is customarily enjoyed by all — is not permitted. Burning incense is regarded as exotic and not included in the permission to engage in kindling a fire on Yom Tov.
The question is thus if smoking is considered “shaveh le-chol nefesh.” The Korban Netanel (Beitzah 2:10) argues that smoking is not included in this category, noting that if one who is not accustomed to smoke were to begin smoking on Yom Tov, he would become ill and disoriented. This demonstrates that smoking is not shaveh le-chol nefesh.
The Chayei Adam (95:13) also prohibits smoking on Yom Tov, but the Biur Halacha (511:4 s.v. ein osin) notes that many Acharonim (including the Chacham Tzvi, cited in the Shaarei Teshuva 511:5 and the Pnei Yehoshua, Shabbos 39b s.v. omnam) permit smoking on Yom Tov. The Biur Halacha notes that those who rule leniently point to the fact that “now that many people are accustomed to this, it has become shaveh le-chol nefesh.” [See also his comment about the possible distinction between the first and second days of Yom Tov, and see Aruch Ha-Shulchan, Orach Chaim 511:11.]
In the modern day, after it became clear that smoking is harmful to one’s health, many poskim argue that the practice can certainly not be considered shaveh le-chol nefesh, and Rav Simcha Bunim Cohen (The Laws of Yom Tov p. 106 footnote 1) thus writes that “In the United States it should certainly be forbidden to smoke according to all opinions, as the overwhelming majority refrain from smoking.” He likewise cites (page 108 footnote 3) from Rav Shlomo Zalman Auerbach (Minchas Shlomo 2:58:6) and Rav Shalom Yosef Elyashiv as ruling that today it is forbidden to smoke on Yom Tov. Rav Zalman Nechemia Goldberg also writes that it is prohibited to smoke on Yom Tov in our times (see Pe’er Tachas Eifer p. 52).
See, however, the posthumously published volume of Iggros Moshe (Orach Chaim Vol. 5, no. 34 ) where Rav Moshe states (in 1984) that it is difficult to proclaim cigarette smoking as prohibited on Yom Tov since millions of people throughout the world smoke.
Overall, based on the opinions of modern authorities, it seems that one should certainly avoid the practice on Yom Tov.