I have wood chips and various yard waste that I add periodically - dry leaves, mowed grass, weeds etc. I’ve had this setup for 4 years and haven’t cleaned it in that time. It composts in place and doesn’t smell, get muddy, or freeze in winter. It’s great!
Dig a hole and keep adding to it. You can temporarily cover the hole and then open it up to add to it. It will compost over time. But why do you have to clean out poop every day? That sounds like a lot of work, and will require an active pile/hole/bucket etc. that you need to access every day...