I have searched for things about Gauss's use of Latin that might bear on the question, these can be found with Google:
The first is this, from Bell's 'Men of Mathematics':
' ... the supple Latin in which many of his greatest works were written. It is an ever-to-be-regretted calamity that even the example of Gauss was powerless against the tides of bigoted nationalism which swept over Europe after the French Revolution and the downfall of Napoleon. Instead of the easy Latin which sufficed for Euler and Gauss, and which any student can master in a few weeks [! I'll be charitable and assume Bell means students that have already been exposed to classical Latin], scientific workers must now acquire a reading knowledge of two or three languages in addition to their own. Gauss resisted as long as he could, but even he had to submit when his astronomical friends in Germany pressed him to write some of his astronomical works in German.'.
I think Bell is distorting things at least somewhat when he says that Gauss really wanted to write in Latin: after 1801 almost all his personal notes were in German, and many of his Latin works were first drafted in German.
The second is a letter (in English) written by Gauss's grandson that mentions the publication of the Werke. He says that they will be difficult reading, but adds to clarify that it is not because of the Latin but the mathematics; so I suppose one could still assume in 1866 that Latin was sufficiently understood.