What you were thinking of sounds really neat! But a little hard to manage as an oekaki adopt. =)
I'm not planning on adding any activities (like exploring) at the moment. Maybe in the future as a special event?
Right now what I am thinking is every month or so there will be a prompt for owners to reply to. Something like, "It's a really rainy season this year. How does your horse keep dry?" And then users may draw or write a story about their horses finding shelter, using magic, or just flipping the prompt around and in this case enjoying being out in the rain. xD Every user that completes a prompt for the month gets x amount of currency.
I haven't decided what the currency is yet, haha. Gold? Magic gems? Something like that. So say maybe you get five gold for one month's prompt.
There will be a thread that acts as an item shop! There might be usable items there like MYOs or trait tokens that can be applied to your pone, and decorative items like the class items or companions. Maybe a wolf puppy companion costs 10 gold, so you'd have to save up two months' prompts to afford it!
There might also be future events that reward items. Something like, say around Halloween there's a Trick-or-Treat special prompt, and the prize for it instead of currency is a black cat, or a witch's cape. I'm not thinking too hard about that stuff yet and trying to stay focused on the core mechanics right now though.
