Emotions are not controllable or choosable but our reactions to them are trainable. One good technique for this is mindfully observing and labelling the emotion until it goes away; not trying to change it but also not acting on it. With practice one can observe the emotion subsiding within a minute or so. This, eventually, leads to less emotional reaction overall because we're taking away the habitual pattern of the mind to constantly react to everything it likes or dislikes.

You are controlling your emotions with that technique, accepting and waiting emotions out is just not the only option.

Getting indoors from a cold rain is an obvious choice. I can't really decide to stop shivering, but changing my clothes and grabbing a hot chocolate helps. It still takes a while to warm back up, meanwhile I can actively choose not to open windows or go right back in the rain.

Yes, you can try to set up the right conditions for the emotions to subside which is non reaction but you can't choose when they subside or when they arise. I read OP as saying that you can directly choose which emotion you experience and when you experience it.

Yeah, this is what I meant. I used to let anger sit with me for hours and derail most of my day.

But now I'm better at deciding to let negative emotions go and feel happy or calm.

Making choices to change your situation will change your feelings so I do believe feelings are a choice to be made in most situations.

No, people are not choosing emotions. You can show them or not, but it is not true that one "chooses" them.

A popular perspective is that emotions are the result of quick analysis of a situation, trained on survival instincts originally but later mostly pattern matching and beliefs. By observing emotional reactions you can drill down to the underlying belief, and over time adjust to new circumstances. For example, based on this theory, anger is the result of an analysis that determines that something is deemed wrong and it is within your power to change it (or extract yourself from the situation). If it’s judged to be not within your power, the resulting emotion is sadness. And these judgments can be changed to have a different emotional experience - beyond feeling them or acting on them. This adjustment requires to identify the original deep pattern/beliefs, not just surface-level desire to do so. This introspection typically requires third party assistance, available in various therapeutic and coaching settings.

My favourite example from my own experience is cycling through hail. I used to hate it. It made me miserable. My face hurts. My body is cold. I just want to die.

Once I started playing around with the ideas of Stoicism, I decided to try an experiment. The next time I got caught out by hail while cycling, I raised my fist up in the air and said "fuck you Universe, this is exactly what I wanted, you fell for my plan!".

I felt a lot better. I like to think of it like the Sith in Star Wars. Whenever they get their butt kicked, they go "It is as I had forseen!" I no longer get surprised by events.

That comparison to the Sith is great! I'm going to try to adopt that approach in my life. If nothing else, it will keep me amused, which is worth something.