My Brooks came with a great waterproof cover.
You can definitely ride it in the rain....your @rse has it well covered while youre riding. I rode 9 days in a row in the rain when I went around Tasmania.....no problems. At night or when I stop I put the cover on it, or I always have a plastic bag or 2 in my bar bag which also works fine.
Wonder why great hiking / trekking boots are leather?? Same deal with a Brooks Saddle.....once broken in and well looked after, they last ages and are super comfy - imho ofc.
I still have a pair of full leather Asolo hiking boots bought in 2006 going strong.
I know that they are not everyone's cup of tea, but most long distance tourers I know and have met on my tours use a Brooks.
Horse for course and all that....