In many cases, the emoticon/emoji/smiley is marked - it is not the default, it stands out in some way. (Wikipedia's article "Markedness" gives a reasonably good overview of what "marked" means here.) But in some cases, use of emoticon is almost formalised - in certain groups of people, certain online communities, not using a smiley or other emoticon is a bit like not saying "please" or "thank you". So in those contexts, the absence of the emoticon is marked, like when I ordered a cup of tea in Paris a couple of weeks ago, and I was so preoccuppied with how to pronounce the word for "tea" in French that I forgot the "s'il vous plait", and the barrista gave me a brief lecture in politeness. I think this contrast between perceiving the smiley as marked, or seeing its absence as marked, is at heart of a lot of misunderstandings over emoticon usage, and a lot of the irritation.

I would guess that since your T used a smiley in her email, she would not be bothered or annoyed by your emoticons, and I think your explanation is perfectly fine. Different people use emojis for different reasons, even though there are some general trends (and it's those trends that researchers can investigate).

Btw, one reason why some people use "lol" and similar abbreviations instead of emoticons is the fact that the emoticons have become so commonplace as to lose some of their meaning. (That is one reason - there are other reasons as well.)

Hmm, I think I had another thought about this as well when I started writing, but it's fallen out of my brain - I'll get back to you if it comes back to me.