We say the "tal" (dew) prayer at musaf on the first day of Pesach, inaugurating the season in which we no longer mention rain in the amida prayer. However, this is immediately relevant to only "mashiv haruach umorid hagashem" in the second benediction of the amida: the request for rain in the ninth benediction of the weekday amida is, well, only on weekdays, so its cessation is effective, practically, only after the first day(s) of Pesach, at the maariv prayer on the first day of chol hamoed.
In most people's versions of the ninth benediction, only a few words change in the middle depending on the season: the beginning of the benediction is constant.
If someone mistakenly starts to say the weekday amida at mincha on a holiday or Shabas, he is supposed to complete whatever benediction he finds himself amid, and then switch over to the holiday amida.
Suppose, then, someone mistakenly starts to say the weekday amida at mincha on the first day of Pesach, and catches himself after starting the ninth benediction. he should, of course, continue it. Should he recite the wintertime request for rain in it, perhaps because no one has yet begun the summertime version of the blessing, or should he not, perhaps because the summer prayer season's already been inaugurated?
We begin the ninth benediction's request for rain on a particular date in the fall. (This date varies by location.) Suppose the date falls on Shabas, and someone makes that same mistake: he says the weekday amida and catches himself after beginning the ninth benediction. Should he continue with the winter version, since the date for the switch has arrived, or with the summer version, since the community hasn't yet switched?
A sourced answer would be ideal.