Haven't had twins. Did have epidural. Would not advise that you do this.
An epidural will prevent you from moving around (even "walking" epidurals can make it quite hard for you to move your legs, and I have not heard of a hospital that lets patients with walking epidurals actually stand, let alone walk). Being unable to move around may complicate your delivery (it sure complicated mine, and I was only having one baby), leading to a longer and less productive pushing phase, a higher chance of coached "purple" pushing, forceps or vaccuum delivery, or to a surgical section.
If you are committed to vaginal delivery (twins or no twins) I would advise you to minimize interventions in the natural birth process. Ask if the hospital has monitoring equipment that will allow you to move around, if not, feel no compunction about taking the monitor off (if you must give them an explanation, tell them you need to get up to pee). If you feel you can refuse monitors entirely, go for it. Pee at least once every hour (a full bladder can impede delivery). You and your partner should read up on and practice some pain management techniques for contractions. Hire a doula if you don't have one already.
In an emergency, they may have to place an epidural quickly or give you general anesthesia, but I think that having an epidural "just in case" raises your odds of having a c-section so much that I wouldn't do it.
To be honest about my biases, I had the nightmare epidural - it stopped working during the pushing phase, leaving me immobilized, but able to feel all the pain, the baby got stuck behind my pubic symphesis. The only reason they held off on a section was that they'd have to push the baby back in to do it. If there had been a second baby, I don't imagine that would have stopped them.