Is it normal for Wi-Fi to always be on? I have a Nexus 4 running CyanogenMod 10.2.1.-mako. While trying to figure out why my battery life seems to be shorter than usual, I have noticed that my Wi-Fi is constantly on.

Shouldn't the Wi-Fi turn itself off when the phone is not in use? Could this be responsible for my lower battery life? (I had much longer battery life on earlier CM versions)
Wi-Fi is usually turned ON or OFF manually. If it's turned on, and it's not in use or phone is considered sleeping, it's still running.

You might want to check with the CyanogenMod forums if there is any Wi-Fi issue for that version.