Should I refinance my paid-off house if I'm going to rent it?

I have a paid for house. I would like to rent it out and live in a rental property elsewhere for the time being. I'm wondering if owning my house outright will be a drawback since I cannot deduct my housing cost as a renter and I will have to count 100% of my rental income as "profit" (is this correct?). Net-net, it seems that my housing cost remains the same but that my tax liability could sky-rocket from this situation. If I refinance a large portion of the house, can I then deduct the interest cost as a business expense to substantially lower my tax liability? Is there any advantage to having a paid for rental property that I'm not thinking of?