In a cash-out refinance, the money that you take out will not be taxable itself. It's a loan. You don't pay tax on money that you borrow. But you will not be able to deduct all of the interest on the refinanced loan. You can only deduct the interest on the portion of the loan that you use to "buy, build, or substantially improve" your home. That means you can only deduct the interest on the amount that is equal to the current balance before the refinancing, unless you use some of the additional money for "substantial" improvements to the home. See IRS Publication 936, Home Mortgage Interest Deduction, for the details.
If your "acquisition debt" is $160K now, it remains 160K after the refinance, unless you use some of the money for "substantial improvements."
Assuming no improvements, then in the first month, your interest will be 160/245, or 65.3% deductible. In the second month, it might be 160/244 or 65.5% deductible, if your payment included $1000 toward principle. Turbotax will help you calculate this on your tax return.