That's a good question. I don't think an extroverted trainer would necessarily be any better or worse for an introverted horse, or vice versa. Perhaps more suited & suitable for that horse's personality, but if she's a good trainer, she should be working with the horse where they're at, in a method most comfortable & motivating for them, regardless of her personal feelings. Eg. she should be able to 'turn off' her extroversion.
I think it's a case of horses requiring different techniques, rather than harder or easier. So saying, it also comes down to whether they're 'right brained'(fearfully explosive or inclined to 'shut down'), or 'left brained'(cool, calm and possibly dominant, playful types). They are rarely just one 'personality type' either, and can be right, left, introvert or extrovert in different situations.
I have dealt with a large number of horses & found it just as easy to deal with fearful as with calm and assertive types. Until my current horse tho, I'm not sure that I ever had to deal with a right brained introvert that became nearly catatonic(only in some situations). Long story how he got there, but it was not helped by me choosing the wrong people to work with him. I think in retrospect I had had mainly experience with extroverts, who 'told it like they saw it' with clear bodylanguage. His reaction to too much stress was to go very quiet and just put up with anything, apparently very 'obediently'.... until suddenly, out of the blue, for no apparent reason(whatever the final, often tiny straw was), it got too much for him & he would blow up. I had misread this quietness as true calmness, so didn't appreciate just how far I was pushing things until I went too far. Once I learned to recognise his early signs(holding his breath, sucking his tongue, etc!) & mental shut down for what it was, I was able to go back to where he was confident & work more carefully from there. Now that he's again confident and trusting of me, he is actually quite extroverted & not afraid to 'say what he thinks'.... most of the time. I still have to be careful & attentive so as not to inadvertently push or allow him to get too stressed.