No matter which software OS you use, it is important that you keep yourself protected from security vulnerabilities otherwise you can get hacked. Developers of the Metasploit framework, which is a penetration testing software, noticed that updates to the WebView component (the one used by Android's HTML renderer) have been discontinued for all Android versions prior to 4.4 (KitKat) and 5.0 (Lollipop). Google has thus decided to abandon lots of users with older Android devices (all 4.x versions except 4.4), even though the version of WebView in them has security vulnerabilities. Here is what you should do to harden your security.
In Android 4.4, the vulnerable WebView component was finally replaced with its modern successor, based on the more secure Chromium code base. But the former one, used in Android 4.3 and earlier, has had no updates for a very long time! As of this moment, at least 11 working exploits are available publicly with different attack vectors! This is not just slightly unsafe, it is very dangerous.
So, what you can do?
Switch to Mobile Firefox on Android
While it will not protect you from third party apps which use WebView, the main app which you might be using to read the web on your mobile device is your browser. So now is a good reason to switch from the outdated default "Browser"/"Internet" app to Firefox for Android. Firefox uses its own alternate rendering engine and is relatively safe. It is getting regular updates and even supports add-ons in the mobile version. For instance, if you install the "AdBlock Plus" or "Adblock Edge" add-on, it will block AdSense on your smartphone and you will not be affected by the AdWords flaw.