Both are grammatical correct, we italian people omit the subject often just for custom, for example:
Io sono stanco, stasera non voglio uscire
Sono stanco, stasera non voglio uscire
both are correct, but we usually say the last, wheras the subject may be included when we need to put more stress on it:
Io sono quello che porta i soldi a casa = I am the one the brings money home. Here, the speaker wants to stress that he is the only one to work, so he says that HE is working, not other people in the home where he's living.
Anyway, if you start an email writing "Oggi io sono tanto felice" it's not really wrong, to italian people it may just appear too formal or useless to use the pronom "io" in that kind of context.