Same here. 3rd gen iPad latest ios. The wifi is connected but instead of having the wifi icon it shows the LTE. I can turn data off and still have Internet connection on the wifi but the icon is missing. I did do a reboot and it fixed it for a while but has done it again.
I'm not sure when this started. I just happen to notice it a few days ago. Could it have anything to do with new year? Maybe somehow linked to the "do not disturb" bug, which I'm experencing as well but understand that it should correct itself on the 7th.