Hi-
The first time we remortgaged, we dropped from 8% to 6% 30 year. I remember someone came to our house to sign the papers, so it was pretty convenient. The second time, we were taking out money to remodel our kitchen. We realized houses were overpriced and it would be cheaper to just upgrade our kitchen and stay put. I think that mortgage was a 30 year at 5 or 5.5%. We did this one in early 2009. This time we had to provide a fair amount of paperwork and the house was appraised, but still nothing too onerous. We had to show up at the mortgage company and sign. DH did not make a realistic kitchen remodel budget, so then he got a home equity loan to finish the kitchen. This changed the whole feel of our house and the kitchen is now the beating heart of our home. It was worth it though we were sick to see the debt.
This past summer we remortgaged through our bank to a 15 year mortgage at less than 4% and rolled the home equity loan into it to get the debt PAID.
There are probably articles online that can help you determine what is in your best interests if you are planning to move. Best of luck to you!