I’m not sure if there have been studies that seek to answer your specific question, but the field of sentiment analysis has done studies to try to automate understanding the feelings people express in short messages on social media.
I’d point out, though, that writing is writing. There’s nothing new about text messages – that’s what the telegraph was in the 19th century, and although there was no specific character limit, because the price of sending a telegram was calculated by the word, people tended to write very short, succinct messages where every word counted, just like they do now on Twitter. And even before that some types of poetry were (and are) very short. So I’d say that humans have transferred – or, maybe more properly, transmitted – emotions and feelings by carefully choosing the right words (of any length) in the right order, with the right punctuation…good writing is good writing, in any medium.
So this isn’t anywhere near my area of expertise, but I do have some of my own observations.
We are communicating via writing more now than we ever have done, and a lot more rapidly, and this sort of question becomes increasingly interesting.
I can definitely get a feel for what emotions someone might be trying to convey based on their punctuation, or if they have the energy to write lengthy words and sentences, or are writing sentences with very short mono-syllabic words. However, I can often get it wrong. I over-think a lot! When you ask ‘how are you today?’ and the response is ‘Fine.’, the full stop and shortness might make me think they’re clearly not okay. But in reality it might be that they’re just about to drive somewhere and don’t really have time.
Maybe there is too much variation from person to person? Maybe machine learning techniques will give us an answer?