No updates for consumer versions of Win10. Including security ones. If on October 15th a zero-day exploit is out in the wild, Microsoft would not be obligated to patch it. They may regardless (see WannaCry Malware patch for Windows XP), but it will not be ongoing, and probably not all-encompassing.
The longer you use the machine on win10 after October, the more exposed you are to any exploit found in the existing windows 10 version.
What this post is trying to present is that Linux distributions almost never run into these issues - especially when it comes to running on legacy hardware. If you install Linux Mint today, you'll still be able to update it in october and beyond, for the foreseeable future.
Edit: There will be a subscription option to receive extended security patches from MS for Windows10, but it will not be free, and the price will rise as time passes (similar to win7).