The only effect from the refi is the number of hard inquiries on your account and your total debt, but I believe they count all the inquiries for a mortgage in a certain time period as one (someone more expert than I am please weigh in). Mortgage debt shouldn't be an issue - actually, should be in your favor unless you have had late payments.

Otherwise, I've done apps after refis in the past few years (two properties) and no problems. Will do more next month after another refi.