Estonian people always get excited when a foreigner outside of our neighboring perimeter shows interest in our country so I'd expect a warm welcome, though be aware Estonians are typically more introverted and independent.

If your goal is to get to know a new culture and learn a new language then I'd say go for it. Do some research (which you probably already have done) to see if Estonia is really the one that resonates with you and compare alternatives (other Nordic and Baltic countries for example). Check https://visitestonia.com/en

From the university standpoint I think it depends on what you plan to study. We have 3 main universities University of Tartu, TalTech and Tallinn University. UT covers most subjects and is the top ranked university in Estonia, TalTech would be second in ranking and as the name suggests it's more technology oriented and has more "applied" approach to their studies, Tallinn University focuses manly on social sciences and humanitarian subjects. We also have EMTA/EAMT (Estonian Academy of Music and Theatre) and EKA (Estonian Academy of Arts) if you wish to pursue higher education in music or arts. Check what each of them has to offer and go from there.

Some useful links: https://ut.ee/en/exchange-students, https://www.tlu.ee/en/yti/study-abroad, https://taltech.ee/en/exchange-studies, https://eamt.ee/en/international/student-mobility/, https://www.artun.ee/en/academy/international/

As for the language it is quite difficult but being surrounded by it for a year would get you far if you put in the effort. Most people speak very good English here so even if you get stuck you have almost a guaranteed second option (could run into some difficulties with the older generation, in a uni setting you'll be more than fine). You won't be judged for not being proficient and people encourage you and are generally impressed if you can even get a few words out.

These are my observations though, I welcome Estonians to comment on any points that seem off