The Mishnah (Taanis 1:1) says:
...אֵין הַגְּשָׁמִים אֶלָּא סִימַן קְלָלָה בֶּחָג
...the descent of rain on the festival of tabernacles is to be considered an unpropitious event
The Mishnah (Sukkah 2:9) also says:
יָרְדוּ גְשָׁמִים...לְמָה הַדָּבָר דּוֹמֶה, לְעֶבֶד שֶׁבָּא לִמְזוֹג כּוֹס לְרַבּוֹ, וְשָׁפַךְ לוֹ קִיתוֹן עַל פָּנָיו:
If rains fell...To what can this matter be compared? To a slave who came to pour a goblet for his master, and he [the master] poured a bowl-full [of water] in his face.
We see that it raining on Sukkos is to be viewed as a negative thing. I have this idea in my head that at least the first Mishnah is specifically referring to the land of Israel, which shouldn't expect rain until after Sukkos (I later found that the Mishmeres Shalom (43:1) says this). Other lands rain all the time with no expectation for it not to on Sukkos. The second Mishnah, presumably is a general statement about if Hashem wants our mitzvah performance, and could potentially refer to all lands (even if the first one doesn't).
However, I saw the Aruch HaShulchan (OC 639:20) write:
אמנם כשיוצא מן הסוכה מפני הגשמים – אל יצא ככועס ומבעט, אלא בהכנעה רבה, כעבד שבא למזוג לו כוס לרבו, ורוצה למזוג היין במים, ושפך לו רבו הקיתון של מים על פניו.(והמקור חיים פירש בזה דהמים ממתקין היין האדום, והוא רמז לרחמים הממתק את הדין, ואין מניחין מן השמים. ואמרו שזהו על ארץ ישראל.)
However, when you leave your Sukkah because of rain, don't leave angry and kicking. Rather, leave with great submissiveness, like a servant who goes to pour a drink for his master, or dilute his wine with water, and the matter splatters it on his face. (But the Mekor Chaim explains that the water perfects the red wine, hinting to compassion perfecting judgement, and they in Heaven don't let him. And they said this was about the land of Israel.)
The fact that the Aruch HaShulchan is bringing this Mishnah, even though he lived in exile, shows me he understood it to be referring to all lands. However, maybe again the first Mishnah is only the land of Israel. Does anyone say it's a simman klala/a bad omen outside the land of Israel if it rains on Sukkos? Is this what he means in his last line (it's unclear to me)?