Horn students are certainly always looking for tips that will give them that edge. Studying excerpts with multiple teachers at an advanced level is advantageous in this regard. As an alternative to live lessons, there are now several free video resources that are highly useful for the advanced horn student, as demonstrated by this look at three different video resources on Beethoven 3.
The most recently posted of these is from Eli Epstein, formerly 2nd horn in the Cleveland Orchestra. His excerpt video series is based on portions of a CD project, Orchestral Excerpts for Low Horn. Several tracks are on YouTube for free, including Beethoven 3. I like his approach to this a lot but know I am a bit biased as I did study with him between my MM and Doctoral studies, and studied this very excerpt with him in depth.
Next up is a bit older video featuring Denise Tryon, 4th horn of the Philadelphia Orchestra. Her approach is fair to say a bit different than that of Epstein. She certainly opens up some different angles to work on for improvement.
Finally we go to the oldest of the three videos, posted back in 2013. This one, with Stefan Jezierski of the Berlin Philharmonic, is more in depth (much longer!) and looks at more than just the most familiar excerpt. And actually 2nd horn is not the focus, it is on the first horn materials — but certainly they inform your approach to the 2nd horn excerpts, it is all worth learning!
Credit goes to two of my current students for pointing me toward the last two of these videos above, and for yet more check out the video resources one has put on his website.