So do I really need to be worried about keeping my (new) brooks saddle dry?
I treated it with the wax they provide, but do I have to cover it?
Short answer, IMHO, yes.
Long answer, it may depend on your saddle, your weight, where you ride, how long it rains, etc. I have fenders which help greatly with water from the bottom, and my personal bottom is large enough that I don't worry about brief, light showers. Given a long day of soaking rain, or high heat and humidity that makes my sweat overpower the sponge, I mean artificial chamois, in my shorts, and the saddle can stretch. You can re-tension it with the Special Brooks Spanner (which you should take for a long trip), but you don't want to do that too often, or too vigorously. Crossing Missouri and Kansas, I needed to re-tension every 7-10 days, mostly from the aforementioned sweat.
I recommend the Aardvark saddle cover for the B-17. You can get it on-line several places, including <http://www.lickbike.com/productpage.aspx?PART_NUM_SUB=%271005-00%27>. I like this one because it's stretchy (aka easy to put on), waterproof (at least when new), and you can ride with it (which, unfortunately, impacts the "when new" bit).
Cover the saddle at night, or when stopped if it looks like rain. Takes 5 seconds with the Aardvark (plus the time it takes to pull it out of its hiding place). You can also use a plastic bag -- if it's waterproof enough, and large enough, it can cover your saddle bag, which keeps metal things in there like multi-tools from rusting. It's surprising how much water the thing can absorb during a heavy dew at night, so I learned to cover it any time it spent the night outdoors. It also rains without notice, even in the west. I've replaced one B-17, although after my cross-country ride I wonder if I could have simply re-tensioned and kept riding.
After a few weeks' touring, you'll look at the saddle one day and think, "That looks sort of dry or thirsty." That's when it's time for another round of Proofide.
You'll find people who say they've used the same Brooks Pro for 30 years without covering it, and those who forget to cover it driving in a thunderstorm and say it's stretched so much it's ruined. My experience, described above, is in the middle of those two extremes.
One last thing -- a worn-out, leaking Aardvark saddle is great for securing the cheap, waterproof plastic bag on the saddle when you're hauling the bike on a car rack.