This affects mortgage rates, but not housing prices. If anything, housing prices should decrease a bit as rates go up, since people tend to buy based on monthly payment which is house price + rate.
Therefore, your down payment should be just as effective as it was before, particularly if it's enough to pay for much of the house and keep your monthly payment lower.
Therefore, your down payment should be just as effective as it was before, particularly if it's enough to pay for much of the house and keep your monthly payment lower.