With my 'security hat' on, I'd have to say you shouldn't use anything that's no longer receiving updates. But that would create a lot of e-waste for no reason.
To see if your phone's browser is still receiving updates, you can browse to:
https://emudhra.we-have-a-problem.com/
That has a grid showing whether your browser was willing to connect to sites using the compromised keys. If your browser is using its own cert style and still receiving updates, should be all green ticks. If so, then you can still use the phone for browsing internet. Be aware that using other apps on your phone (like eg. your email app) could be read easily by third parties, especially if you're connected to unfamiliar wifi.
If it's all red, maybe try another browser? Or relegate that device to being a dumb phone - switch off its data connection, phone calls only.
