I always have an umbrella in my backpack, and whenever I'm heading to work, I have my backpack. Simple, no muss, no fuss, I'm prepared.
As for a jacket, seriously, how tough is it to take it with you and wrap it around your waist by the sleeves? If you need it, you have it. Alternatively, if you're wearing it and it heats up, how tough is it, and how long can it really take, to take the jacket off and wrap it around your waist? I was at Johnson Space Center this weekend. THAT is rocket science. THIS is not.
Right now it's colder than hell in the morning and by afternoon it's heating up to the point of feeling meh.
Dealt with the same thing all the time in school in Arizona. Simple solution even us high schoolers could figure out: in the morning, on our way to school, we'd wear a jacket, extra flannel shirt, sweatshirt, whatever. In the afternoon, on our way home from school, when it had warmed up (and the disparity in the desert was often as much as 30-40 degrees
F between the two times of day), we either left said extra gear in our locker, or took it home with us in our backpack.
Okay, I lie. Typically we'd leave it in our locker, because we were lazy, and after a few weeks, we'd have to leave our books behind and take home our locker full of laundry that had accumulated. But still, it wasn't that tough a concept.
Weather changes. How many places have you been where a common local saying is "If you don't like the weather in [Wherever], wait five minutes"? So, we deal with it. Yeah, it sucks that the weather is playing you like a yo-yo, but rise above it, folks.