first Rashi explains that mazkirin is only to give shevach for bringing rain, but not a tefilla like vsain tal umatar. Later he explains that our mishna is going on the mishna in RH that the world is judged on water on Succos, so we mention in order to have a good din. So is it a tefilla or not?
Anon, miami USA
One has to make a distinction between Tefilah and between "Ritzuy" (appeasing Hash-m). RASHI ,in the Mishnah DH LO , explains that R. Eliezer replied to R. Yehoshua that he had not said that one should pray ("Tefilah") for rain on Succos but only that one should mention rain then. RASHI, later on DH VE'EIDEE, writes that since the judgement on water is on Succos, the Tana maintained that this teaches that one should mention the matter of water then, in order "le'Ratzuy" (to appease and praise Hash-m so that he should desire our prayers) about water, in order that the rain should come for a blessing. This is why the Mishnah states that one mentions rain on Succos.
One sees that Rashi did not actually say that one prays for rain on Succos but rather that one finds favor with Hash-m then by mentioning rain. TOSFOS DH ELLA explains further that the normal way is to find favor before one asks for something.
(See Gemara Avodah Zarah end 7b that one always should arrange Hash-m's praise and afterwards pray. This is why we say the first 3 berachos of Shemoneh Esreh which only praise Hash-m. This includes "Mashiv Haruach. Only afterwards do we request our needs from Hash-m). Therefore we praise Hash-m for the great gift of rain before we actually pray for it and request it.
So Mashiv ha'Ru'ach is not a Tefilah but rather a preliminary to tefilah.
KOL TUV
D. Bloom