I'm in zone 7a, Middle Tennessee, and we get a nice amount of precip during the winter months. I have three woody ( "tree") peonies one pots that I leave out the entire year. I have inverted a pot over the top during ice storms, and during high precipitation events in the winter months.
I also have three herbaceous peonies in pots that weren't what I paid for. Two look great and one looks bad. They have been in those pots for three years, with no extra attention. I'm going to use their roots for graft stock when I try to graft some woody peonies.
Top and Liz's suggestions to shelter your pots makes the most sense in your zone.
