Gemara

Mishnah: Women are exempt from a Mitzvas Aseh sheha'Zman Gerama (it applies only at certain times).

33b (Beraisa): The following Mitzvos are Zman Gerama: Sukah, Lulav, Shofar, Tzitzis and Tefilin;

Chagigah 16b (Rami bar Chama): Semichah (pressing on the neck of a Korban) must be with all one's strength.

Question (Beraisa #1): "Daber El Benei Yisrael... v'Somach" - Benei Yisrael do Semichah, but Benos Yisrael do not;

R. Yosi and R. Shimon say, Semichah is Reshus (optional) for Benos Yisrael.

R. Yosi: Once, they brought a Shelamim to the Ezras Nashim for women to do Semichah on it, just to please them. Semichah does not apply to women.

If Semichah must be with all one's strength, we could not allow using a Korban (to support oneself on it) just to please women!

Answer: The women were told to do Semichah softly.

Rosh Hashanah 33a (Mishnah): We do not stop children from blowing a Shofar (on Rosh Hashanah).

Inference: We stop women from blowing.

Contradiction (Beraisa): We do not stop women from blowing.

Answer (Abaye): The Mishnah is like R. Yehudah (the first Tana of Beraisa #1 above). The Beraisa is like R. Yosi and R. Shimon:

Eruvin 96a - Beraisa: Michal bas Sha'ul used to wear Tefilin. The wife of Yonah (the Navi) was Olah l'Regel. Chachamim did not protest against either of them.

Inference: They did not protest against Michal because they held that Tefilin is Mitzvas Aseh she'Lo ha'Zman Gerama!

Rejection: Perhaps the Tana (holds that it is Zman Gerama, but he) holds like R. Yosi, who says that Semichah is optional for women. (The same applies to every Mitzvas Aseh sheha'Zman Gerama, therefore Chachamim did not protest.)

Rishonim

Rambam (Hilchos Tzitzis 3:9): A woman is exempt from Tzitzis. If she wants to wear Tzitzis without a Berachah, she may. Similarly, if she performs any Mitzvah from which she is exempt without a Berachah, we do not protest.

Hagahos Maimoniyos (30): Chachamim did not object to women who fulfilled Mitzvos from which they are exempt (Eruvin 96a). Michal wore Tefilin and Yonah's wife was Olah l'Regel. The Yerushalmi says that Chachamim objected. I heard from a Gadol that we protest only where there is concern for transgression, e.g. Chulin ba'Azarah, Ervah (her hair might show), or blowing a Shofar on Rosh Hashanah, which is Shevus (if it is not a Mitzvah). Where there is no concern, such as Sukah and Lulav, we do not protest.

Note: Women may bring Nedavos! Perhaps the concern is lest she say 'this is my Olas Re'iyah', and since she is exempt, it is Chulin. Ma'aseh Choshev (on Sha'ar ha'Melech Avodah Zarah 12:3, 30) says that she brought Olas Re'iyah on Yom Tov, when Olas Nedavah is forbidden. Tefilin is not a problem of Ervah for single women, whose hair may show, or even for a married woman who shaved the hair there or totally covered (the Tefilin and) her hair. (Tefilin Shel Rosh should be exposed ("V'Ra'u... Ki Shem Hash-m Nikra Alecha... - Menachos 35b), but this is not essential.) Perhaps R. Yehudah always forbids, lest a married woman's hair show. The Ran (Rosh Hashanah 9b DH ul'Inyan Halachah) learns from Michal and Yonah's wife that women may blow Shofar; we are not concerned for Shevus or Bal Tosif. Seemingly, these are concerns also regarding Lulav (it is Muktzeh).

Rambam (Hilchos Shofar 2:1,2): Women are exempt from hearing the Shofar. If a woman blew a Shofar, one who heard was not Yotzei.

Hagahos Maimoniyos (1): Just like women may do Semichah, even though it looks like Avodah with Kodshim, they may blow, even though it looks like Chilul Yom Tov. A man who was already Yotzei may not sin to please others.

R. Mano'ach (2): We learn from this that women may blow without a Berachah. Similarly, Chachamim did not object to Michal and Yonah's wife for wearing Tefilin and being Olah l'Regel. The Rambam (Halachah 7) brings the Heter for children to blow a Shofar on Rosh Hashanah; he does not permit women. The Halachah follows our Stam Mishnah against an argument in a Beraisa (R. Yosi and R. Shimon). Also the Rif brings the Heter only for children, but not for women.

Note: R. Mano'ach retracted from his initial words. The proof from Michal and Yonah's wife is like R. Yosi, but R. Yehudah holds that Chachamim protested. However, the Rambam (Tzitzis 3:9) says that we do not protest if women perform any Mitzvas Aseh sheha'Zman Gerama. Perhaps he holds that it is not clear whom the Halachah follows, therefore we do not protest.

Rosh (Rosh Hashanah 4:7): R. Tam says that even though our Stam Tana is like R. Yehudah, the Halachah follows R. Yosi, for Nimuko Imo (he has great reasons to support himself). Also, Michal wore Tefilin and Yonah's wife was Oleh l'Regel. Since actions were done, we follow them. Also, a Shelamim was brought to the Ezras Nashim for women to do Semichah on it to please them. Ba'al ha'Itur says that they may blow for themselves, but a man may not blow (just) for them. The custom in Ashkenaz is that a man blows for women before they blow in the Beis ha'Keneses, so he himself is Yotzei then. Avi ha'Ezri says that since women may do proper Semichah, even though it looks like Avodah with Kodshim, similarly a man may blow for them. Teki'as Shofar is a Chachmah. It is not a Melachah.

Rashba (Rosh Hashanah 33a DH R. Yosi): Our Mishnah is not a Stam Mishnah teaching that only children may blow, but not women. Rather, it permits children, for all agree about them. It does not discuss women, for Tana'im argue about this. However, this is wrong. The Gemara learns from our Mishnah that R. Meir holds that Semichah is not Reshus for women!

Poskim

Shulchan Aruch (17:2): A woman is exempt from Tzitzis because it is Mitzvas Aseh sheha'Zman Gerama.

Rema: If she wants to cover herself (with a Talis) and bless, she may, just like any Mitzvas Aseh sheha'Zman Gerama.

Beis Yosef (589 DH v'Af and DH v'Chosav ha'Rav): The Ran and Rosh say that just like women may do Semichah, without concern for Avodah with Kodshim, they may do any Aseh sheha'Zman Gerama, without concern for Bal Tosif or Shevus of Teki'ah. R. Yeshayah says that if a woman blesses, she shows that it is a Chiyuv, and she transgresses Bal Tosif and a Berachah l'Vatalah. Regarding Bal Tosif, this is not true.

Rema: However, this looks like haughtiness. Therefore, she should not wear Tzitzis, since it is not an obligation on the person. I.e. one need not buy a (four-cornered) garment to become obligated.

Mishnah Berurah (5): The Rema teaches why women do fulfill and bless on Lulav. Tzitzis is different, for it is not obligatory even on men.