Good Lord, why would you do that to yourself (or the horse)? Mine hate the wet and wind (Spanish, donncha know...). I'm old and have spent more than enough time getting soaked/frozen/sweaty/filthy/sore/battered in my life.
I ride regardless. Not because I want to but because I am paid to. Though I do spend an awful lot of winter in a stable clipping watching the weather outside knowing I would rather be hairy than out in the awful weather!
I have an indoor so I ride whatever the weather. The surface isn't great so it will be slower work and no jumping but it makes it easy to keep mine fit for hunting and competing.
Despite that the weather doesn't bother me too much. I have good waterproofs so I ride outdoors in the rain if I have a lesson or at the weekend when I want to hack.