Our air conditioner sits outside near the house, the hose that is connected to it is completely covered in ice. It is nearly 70 degrees, could this mean a possible leak or anything to worry about?

Yes it is something to worry about. I would suggest sutting unit down until problem is corrected. Means a leak, lack of air flow (dirty coils/ fan motor no running proper speed) Is the compressor and both indoor and outdoor runnig?

I shut the unit off but it is still running outside?

Shut off at the disconnect outside or breaker box inside