If you can write an interesting poem about winter while riding on a horse, I’ll be pretty surprised. It’s hard enough to write a poem as it is, let alone an interesting one. And then you’re riding on a horse and the poem has to be about winter? Heck, I’d be surprised if you didn’t fall off the horse and injure yourself.
You might also be surprised to learn that you are to ride this horse all across きょうと. That gives you a time limit. You have until you traverse きょうと to write this poem about winter.