In the windows world there is Shadow Defender which makes it trivial to manage non-persistent drives. Any hard drive partition can be made non-persistent by Shadow Defender transparently logging what is written to it so it can be undone at the next reboot.

What is the easiest to manage equivalent in linux nowadays?

Mount a directory using tmpfs.

Forgot to say, this is of interest for the system partition.

Can a ubuntu derivative such as peppermint linux be installed so the entire system partition is mounted using tmpfs at boot time?

Isn't that how all livecds work?

Yes but how do you install to a hard drive so it works like a live CD? Also how do you update? Shadow Defender offers a feature where you can disable it temporarily so you can apply the updates.

With Ubuntu derivatives like Peppermint, you can put the iso file on a Linux or windows partition and boot the iso. Of course, you would need Grub2 installed somewhere to boot as windows bootloader isn't going to boot it. The link below explains it and includes some example menuentries:

https://help.ubuntu.com/community/Grub2/ISOBoot

Update what? If you want to add data, you just mount a partition while booted to it and copy it there. If you mean update software, you don't as it is a read-only filesystem. One exception is if you make it persistent by creating a casper-rw file or a separate Linux casper-rw partition. Quite simple on flash drives, I've never tried it on a hard drive but the Ubuntu link below discusses it.

https://help.ubuntu.com/community/LiveCD/Persistence

1. Install the base-system
2. Make sure that you have a kernel that supports an UnionFS, like overlayfs (already built into the kernel by default on Ubuntu)
3. Create an initrd and alter its scripts so that they mount a tmpfs over the base-system using the UnionFS.
4. Change the scripts in the initrd that they now use the newly created UnionFS as root filesystem.

Now any changes made to the system will be made in the tmpfs only, just rebooting the system will clear all changes. To update the underlying system just mount the partition, chroot into it and do the updates.
On systems with low memory you might want use a second partition instead of a tmpfs, just make sure you delete all files (or simply format it) before (or after) it is used.

Puppy Linux might suit. You can do what they call a "frugal install", with the Puppy image on your hard disk but copied to RAM disk when it boots. That way the working version disappears when you shut down.

I guess any modern distro could be made to mount with some fuse or aufs then changes destroyed on reboot.

Many live distros could be installed and some have a feature like toram or other names to run completely from ram.

I think the latest beta of OpenSuse offers to boot from snapshots so maybe something like that or even some filesystem like btrfs or qcow might work.