Just going to throw out there that preferred form of communication is going to vary everywhere that you go. I am a barn manager and instructor, and I do 95% of my communication via email. Boarders and the few lesson students who have my phone number know that texting or calling is for absolute emergency only.
Here is my reasoning for this, and it is two-fold. First, texting always feels like a “right now” communication. Meaning if I text someone, I’m expecting a pretty quick response, and therefore keep it for personal communication. When someone texts me with a question, I know they want communication pretty quickly. With email, it feels like more common knowledge that it will be checked and answered within a couple hours - even though I get the emails on my phone as well, I can put it to the back of my mind and answer when I have time to actually sit and formulate a response. Secondly, and this is very personal preference, I much prefer to type things out, with plenty of information, that can’t really be misinterpreted. I can’t do that in a text without it becoming a novel (kind of like this response is becoming). This is also why I prefer email over phone calls, especially in the beginning, because I want to think carefully about what I am saying and be able to reread and edit when necessary. I’m a very visual person, and being able to see the words helps me formulate a response as opposed to following along with a auditory phone conversation. I also have a tendency to lose texts whereas I can go back in and easily search or look at the computer screen to find an old email.
I will say, when I am trying to vet a potential new rider over email, I ask a couple pretty specific questions, including day and times available, previous riding experience, whether the rider has been riding consistently recently, and approximate height and weight, so that if all of the other boxes check out, I don’t end up with a rider coming for a lesson and realizing that I don’t have a suitable horse for them.
OP, without sharing your contact info from the email, would you feel comfortable posting what you sent, or a version of what you sent? It might help some of us give a suggestion if there is something in your communication that is giving red flags.