I’ve Poncho’d up in the rain, and it’s been fine. Love it when everything’s a walk on! Last trip it was pouring, we just shrugged and grabbed (then ate) a dole whip in the rain while the rest of the park scurried for cover.
However, true Florida-style torrential rain, we duck inside shops or restaurants. And if it’s going before we set out, we’d stay at the hotel until (or if) it blew over.
Oh how I wish we had thought to bring one of these last time! We gave our stroller to the CM in line for KS in AK and it started raining while we were riding. When we got out, it was completely drenched. Later that same trip, we put our stroller under an awning (in legitimate stroller parking area) but it was moved by a CM to an area that was not covered and again got soaked. They even pulled back the built-in retractable cover for some reason. 
Was SDD closed? I have heard they close it during lightning but curious if it’s just rain. (Although I think in Florida, unlike DL, the two almost always go hand in hand, even if you don’t hear thunder nearby.)
Torrential rain?
If it wasn’t posing some danger, I’d gear up (or maybe even down, if it was warm enough) and then I’d go out and enjoy it - probably wind up being a highlight of a trip. We got to experience DHS at the tail end of a BAD rain last time. We were actually swimming at the resort when the skies opened up. The pool closed, we got all snacky in the room while very closely monitoring the weather and fastpass hunting. Then we geared up and headed over to DHS about an hour before the weather was supposed to let up. Had a blast. It wasn’t a ghost town, but there were definitely very low crowds.
For me the decision would be tied to the time of year. Soaking at 70 degrees is different than at 50.
I don’t think SDD was closed, but I don’t remember for sure because we never intended to ride it.