Some people say it is more difficult to play slow than to play fast. I would say it depends how slow and how fast we're talking about. Having said that, we need to play slow movements pretty much all the time so we should spend some time practicing it.
It is easy to neglect slow music because we'd rather spend more time practicing virtuoso passages. This is a mistake in my opinion because most of the orchestral excerpts you will have to perform in auditions are either slow movements or aren't that difficult for the fingers. Sure, you'll see a few fast ones and by all means, you should practice them but the fact is that you are most likely to be asked to perform passages that will showcase your tone, intonation and musicality rather than your ability to play fast.
When you play slow music, there's nowhere to hide so you need to make every note beautiful and in tune and think about a nice phrasing. This will greatly benefit your playing and you'll sound better, be more in tune and musical at all speeds.
Take the slow movement of any concerto, a slow piece or an etude of your choice and make it sound great. It won't be easy in the beginning but the more you do it, the better you'll become at it. If you practice slow music regularly, playing slow excerpts will become second nature for you.
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.