R’ Eliezer says we start saying ‘ Morid Hageshem’ [who brings down rain] in the second bracha of Shmone Esrei on the first day of Succos. R’ Yehoshua says we start on the last day of Succos.

R’ Yehoshua asked R’ Elezer, ‘If rain is considered a curse on Succos, why do we mention it at the beginning of Succos’. R’ Eliezer answered back, ‘I didn’t say to ask for rain, I just said to say the praise of Hashem that he gives rain.’ R’ Yehoshua answered back, ‘If so, you should always say it not only near the winter.’

Taanis 1:2

R’ Yehuda says that the chazon that says mussaf on the last day of Succos says ‘ Morid Hageshem’. On the first day of Pesach the chazon during shacharis says ‘Morid Hageshem’, and the chazon by mussaf stops saying it.

Others say that R’ Yehuda holds that you say ‘vsain tal umatar’ until the end of Pesach. R’ Yosee says until the end of the month of Nissan.