You can upgrade your Linux Mint install w/out a reinstall, if the Update Manager shows under 'Edit', there's a new release. The upgrade will take only 5-20 minutes, depending on your ISP speed & power of computer (the more CPU & RAM, the faster everything is). Older CPU's & those with small amounts of RAM (such as 1 to 2GB of DDR) may see increased update times, yet at the same time, I wouldn't expect an optimal Cinnamon experience on that type of computer.
Being that I don't have Cinnamon, don't know if there's an upgrade for it or not, however the Cinnamon core may be offered as an update just as the Linux core is, and I get frequent Linux core updates.
After reading the article, just keep looking for 17.3 to be offered through the Update Manager (under 'Edit'). I'm still running MATE 17.1 because I had unfixable issues with upgrading to 17.2, though the 17 to 17.1 upgrade was seamlessly perfect. This was the way Linux Mint 17 was setup, for the rest of the point releases to be upgraded through the Update Manager, all are based on Ubuntu 14.04, and that make it possible.
Now next year when Mint 18 is shipped, usually 2-3 months for MATE/Cinnamon, after the Ubuntu 16.04 release, you'll need to clean install at a minimum, your main or root partition. You can & should for best cleanup of your /home partition, transfer the items you want to keep into a folder on an external (or spare internal) HDD. If that's formatted as NTFS, that's OK, the items can be dragged to the folder & dragged back once it's fully clean installed. There's a lot more to the /home partition than the 8 folders under your user name. A lot of old directories, uninstalled items that weren't cleaned up, you'll just have a better experience by the clean install of every partition. The OS will also run faster, too.
Usually for these point releases (what 17.3 is) that doesn't matter. There may be one or two more point releases before Mint 18 ships around May or June of next year, and 17.3 may be one of those. I've yet to read any news about it for MATE, though will now check it out, usually both Cinnamon & MATE will upgrade together, unless there was a release to the Cinnamon core that would trigger an upgrade for that OS only.
Once I purchase my next upgrade, am going to be doing some clean installing of all of my OS's, setting the PC back to factory GPT settings for the added performance, and just leave Secure Boot disabled. At the time I purchased the PC, wasn't yet a member of this forum, though was & still one on the Dell forum, one member saying to install Windows 7 or Linux, that Secure Boot had to be disabled & a couple of other items changed, one was going from GPT to MBR, I don't believe this was necessary & has cost me performance, as i've only disabled Secure Boot on some computers for others & was able to perform a Linux install. Or downgrade to Windows 7 (many sees this as an upgrade).
As far as you first question goes, actually Linux Mint doesn't upgrade that fast, it used to be that an OS install was needed before Mint 17, and the OS's that weren't LTS were supported for 9 months or so. That's why Mint 13 is still supported for about 16 more months, and 14 through 16 aren't, Because these were short releases. Clem (the Linux Mint founder) decided to do it this way (kind of like a Service Pack), rather than wait for Ubuntu to release it's next OS, and then a new short term release would be issued. The way it is now, there's no set time when the OS is upgraded, yet when there is, it's normally a painless update & includes OS enhancements & bug fixes.
Hope that this helps to explain.
Good Luck with Cinnamon 17.3 when it ships!