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Not sure how it will affect you. The rules are a little different if you are refi'ing a second home.
My suggestion would be to call the current lender and ask them about refi'ing, as well as calling other lenders to get a feel for the scenario.
Why do you want to refi?
I have two homes, spend about equal time in each. My DW/co-owner spends well more than half-time in the one that I refinanced, so I thought we had a good case for it being the primary home. However, the other house is near my job (which is the only reason for owning it). The lender I preferred told me their policy for multiple homes was to consider the house closest to your job to be the primary home. (What happens if you have two jobs, too? I dunno.) There was no rental involved in my situation.
So I had to apply for my re-finance as a second home. Didn't have too bad an impact, though. They charged me a quarter-point extra. Sort of. They also had a quarter-point premium for a no-escrow arrangement, but only actually charged me one of those quarter points.
Shop the interest rate and the closing costs with other lenders too.
Here in Florida we have many people with second homes and usually there is no bump in the rate for a second home.
Now the escrow waiver fee is normal.
You may end up with the same lender, but if they know you are shopping, they have a tendency to offer a little better rate IME.