My response to a bit of paper like in the OP would be to toss it in the wood stove.
I was wondering the same thing.
I prefer pit toilets. Paper is no problem so long as I have enough. And I never need worry about my drooping balls sloshing around in slush. That’s why I hate most modern flush toilets - they’re unsuited for older guys. Try wiping your butt with one hand while the other holds your balls out of the goop at the WalMart restroom. Have fun. 
An artistic sort might eat beans, crap, wipe with tissue, leave the tissue in place, fart, light the fart, and feel the tissue burn. Go ahead, try it. Don’t send me the video.
Another post that makes me glad I’m a woman… while I have droopy bits they get nowhere near toilet water during normal operations.
This. I’ve tried tissueless blowing a few times and the majority of the time involved at least a persistent hanger if not a full-blown upper lip of snot.
The trash is incinerated, and I believe the leftover solids are also incinerated, so there’s not much difference.
What might be different is to use fabric handkerchiefs, which can be used for multiple nose blows (if they aren’t too messy) and then go in the wash. Less paper product coming into the house, and less paper product leaving the house.