According to Rabbi Dovid Ostroff Shlita
The Rama in Hilchos Succah 626:3 says that one is permitted to open and shut hinged flaps that are used for covering the Succah when raining. The Chazon Ish 52:6 learned from here that this would likewise apply to a canopy connected to a baby carriage. Since the canopy is attached to the baby carriage before Shabbos, it has the same status of being open a tefach before Shabbos and one is permitted to fully open the canopy on Shabbos. The same would apply to a canopy covering.
Igros Moshe Orach Chaim 4 - page 194, Ohr L'tsion however do not agree to this analogy and in order to permit the extending of a carriage’s canopy on Shabbos they require the canopy open a tefach before Shabbos. As usual one should therefore ask one’s rav as to how to conduct oneself on Shabbos. Rav Sternbuch Shlita said that the custom is to be lenient.
My question is regarding a unattached plastic cover which people use when it is raining. What would be the Halacha with such a plastic? Igros Moshe Orach Chaim 5:39:4 says that one may put a plastic cover on top of a succah on Shabbos. This is not called "construction", because the cover is clearly temporary. Would one be allowed to open it and place it on top of a stroller on Shabbos and/or Yom Tov as it is also clearly temporary or is it considered an Ohel and prohibited?