What is your car loan interest rate? If the rate is higher than 5% and you do have the cash to pay off the balance, then go ahead. But you just mentioned using your rewards credit card? That I wouldn’t do. You are proposing to change bad debt (car loan) into the worst debt (credit card).
Part of your house buying strategy should be reducing debts to a minimum. Credit card debt is the first one that must go. Then car loans, then student loans. If you think you’ll need a new car in the future, consider buying a used car for cash.
(I bought a brand new Camaro in 2001 for 16K after taxes. My brother just bought a used Camry with only 57K miles on it, for less than $5.5K; I think he got a much better deal. New cars are a expensive indulgence.)
Finally, don’t deplete your cash reserves for the sake of paying off the car loan: if an emergency arises, it’d be good to have some cash on hand.