It would be inappropriate to give financial advice without knowing a person’s complete financial situation and goals, but why do you think you will be able to refinance at a lower rate when you retire since interest rates are unpredictable. In addition, when you refinance the new loan requires that a greater percentage of your payment is applied to interest.
Here are some things to think about. Suppose you have a $100,000 mortgage at 5%. If you have $100,000 in cash lying around, paying off your mortgage would be the same as investing that $100,000 in a very safe 5% investment. If you refinanced the house at a lower rate, could you invest that cash in a way that would earn more than 5%? You might have to use a riskier investment strategy to get better than 5%, are you willing to tolerate the risk after you have retired?
suppose you refinanced at 3%, and put the money in an investment account, and then draw off from the investment account each month to make the mortgage payments. By the time the money runs out in the investment account, you may have paid off the mortgage. If the investment earned 7%, you would be a net 4% ahead. On the other hand, if the investment earned less than the mortgage, then you’re falling behind.
On the other hand, if your house is in a neighborhood that is “going downhill“, then that investment might lose value over time, and you would be wiser to just make simple mortgage payments until you are ready to move, and invest the cash elsewhere in the mean time.
If you ever needed money in a hurry, most of the things you would invest in would be easier to cash out than your house.
If you have cash lying around and you are eligible to invest in a Roth IRA, that also might be an interesting choice because you can withdraw the money in the future tax free if you hold onto it at least five years. In regular investments, you will pay tax on the yearly interest and dividends and you will pay capital gains when you cash out.
Only you can decide what is best for you, possibly after consulting a professional financial advisor.