The question starts with when you can fulfil someone else's obligation by saying a blessing for them. The Rambam (Brachot 1:10) writes (based on Bavli RH 29):
כל הברכות כולן, אף על פי שבירך ויצא ידי חובתו, מותר לו לברך לאחרים שלא יצאו ידי חובתן, כדי להוציאן--חוץ מברכת ההניה שאין בה מצוה, שאינו מברך לאחרים אלא אם כן נהנה עימהן. אבל ברכת ההניה שיש בה מצוה--כגון אכילת מצה בלילי הפסח, וקידוש היום--הרי זה מברך לאחרים ואוכלים ושותים, אף על פי שאינו אוכל ושותה עימהן.
All blessings, even if he [is not currently fulfilling his obligation], he can say for others who have not fulfilled their obligation in order to exempt them -- except for pleasure blessings [Birkot haNehenin] which do not have a mitzva component, where he cannot say the blessing for others unless he is deriving pleasure as well; however, pleasure blessings which have a mitzva component (such as [Hamotzi on] eating Matza at the Seder or [Hagefen on wine at] Kiddush), these he can say for others who can eat or drink without his eating and drinking with them.
The question then becomes, is the blessing on the spices a pleasure blessing with or without a mitzva component. On the one hand, it is part of the Havdallah ritual; on the other hand, the Shulchan Aruch (OC 297:1) is clear that one need not seek out spices, but rather one uses them if they are available and doesn't if they aren't.
The first person I know of to ask this question is Rabbi Yehuda ben Kalonymous, who was anosmic, to Rabbeinu Ephraim of Regensburg (recorded in Or Zarua II 92):
ואדם שהוא תותרן ואינו מריח אם יכול לברך בורא עצי בשמים כדי להוציא אחרים דבר זה כבר שלח רבי' יהודה בר' קלונימוס בר' משה לרבי' אפרים ואני תותרן ואיני מריח כל עיקר אם הוא ברכה לבטלה שאני מברך על עצי בשמים ואני סומך על הוצאת אחרים י"ח והשיב לו אדם שאין מריח ומברך לעצמו על הבשמים יברכה לבטלה היא ואם להוציא ב"ב אינו יכול ולא דמי לקידוש והבדלה וברכת לחם ומצה דהוו חובה ומצוה אבל בשמים אינו אלא מנהג:
One who is anosmic and cannot smell, can he say the blessing on spices for others? This was already sent by Rabbi Yehuda son of Rabbi Kalonymus son of Rabbi Moshe to Rabbeinu Ephraim, "I am anosmic and cannot smell at all. Is it a blessing in vain when I bless the spices, relying on exempting others?" And Rabbeinu Ephraim responded, "One who cannot smell and blesses the spices for himself has blessed in vain. Additionally, he cannot rely on exempting his household, for this is not similar to [Hagefen by] Kiddush and Havdallah or [Hamotzi on] bread [of Sabbath meals?] or on Matza, for those are obligatory whereas the spices are only a custom."
The Tur (OC 297) quotes his father, Rosh, who argues based on the continuation of the Talmud (RH 29) mentioned above which permits saying Hamotzi for one's children "in order to educate them in Mitzvot". So too here, Rosh concludes, where there also is no obligation one can exempt his family.
This position is limited by Rabbis Yoel Sirkes (Bach) and Yosef Karo (Beit Yosef) there to where the children are minors of educable age, parallel seemingly to the case of the bread from RH 29. R Karo however, goes on to posit that Rosh's ruling is correct because saying a blessing on spices at Havdallah is an established enough custom to grant it mitzva-component status, similar to Kiddush and Matza at the Seder. Accordingly, he rules as such in his Shulchan Aruch (OC 297:5).
This innovation of his though is not accepted by most later authorities. Taz and Magen Avraham note that the Shulchan Aruch elsewhere (OC 167:20) rules that the Hamotzi of Sabbath meals (which are seemingly more obligatory than spices at Havdallah) do not have the mitzva-component status. The Gra too seems to reject this. Rabbi Akiva Eiger (here) suggests that even if it is a mitzva, an anosmic is excluded from that mitzva and can't exempt anyone with its blessing. Both Aruch haShulchan and Mishna Berura seem to accept this criticism. Accordingly, it would seem prudent for an anosmic to avoid making the blessing for others (and certainly not for himself), with room to be lenient for one's own minor children.
Two other views in Rishonim:
Orchot Chayim (quoted in Beit Yosef) rules that an anosmic can make a blessing on smells always because they benefit his body even if he doesn't feel it.
Sefer Minhagim (Tyrnau) (Motzash 7, quoted in Magen Avraham) rules that an anosmic can make the blessing on spices at havdallah because he too benefits from smells, because others can warn him of approaching fires based on smells. [A very unique position; compare to Bavli Megillah 24.]
That said, I had a chavrusa for many years who was born anosmic like his father. He reported to me that his father said the blessing for the whole family weekly.
Also worth noting (because you mentioned it) that the Hid"a (Yosif Ometz 17) rules against Rosh, but permits saying the blessing for one's minor children if one is only temporarily unable to smell because of a cold.