What to do with outdated hardware in terms of Meltdown and Spectre
Depends on what your definition of safe is.

If you want to have a guarantee that your computer will not be compromised through the Meltdown/Spectre techniques - no, it is not safe.

If you want to be reasonably sure that the risk of your computer being compromised through the Meltdown/Spectre techniques in the short term is low, then yes it is safe.

Please be advised that even if you do no install new third party programs, you will still be vulnerable through Javascript, Flash and similar on web pages, and through programs that feature auto-updating systems that could potentially download malicious software.

As far as know right know, there is a significant difference between the safety of iOS devices (iPhone/iPad/AppleTV (not first gen)) and Intel Macs. This is due to the fact that the Intel CPUs in the Mac is more susceptible to Meltdown/Spectre than the ARM CPUs in the iOS devices. I.e. more variants of exploits are successful on Intel than on ARM at the moment (considering that you the device is outdated and will not receive any software or firmware updates to mitigate these attacks).