Question:
If the shul is full and the only available place to daven is outside, in an open area that is visible to the public, may one daven there?
Answer:
Yes. Although one should initially avoid davening in an open and exposed area, such as a field or other public outdoor location, nevertheless if there is a need to do so, one may daven there.
Chazal teach that one should not daven in an exposed area, as a more private and enclosed setting helps a person feel the awe of Hashem and pray with greater concentration and humility. However, this is an initial preference and not an absolute invalidation of the prayer. Accordingly, if the shul is full and the only available space is outside, one may daven outdoors. Likewise, travelers who are on the road may daven in an open area when necessary. Therefore, when no suitable indoor location is available, one should certainly daven outside rather than forgo tefillah with the congregation or proper tefillah altogether.
Sources:
Admur 90:5; Michaber 90:5; Rambam Tefila 11:21; Rav Kahane Brachos 34b; Megillah 26a; M”A 90:6 in name of Zohar Beshalach 59; M”B 90:11; Ketzos HaShulchan 20:4; Shulchan Hatahor 90:3; Leket Hakemach Hachadash 90:15; Piskeiy Teshuvos 90:5