I am considering having an outdoor wedding in March, but am concerned about unpredictable weather at that time of year. I can make backup arrangements, but how should I handle this on the invitations? Is it wrong to list a second location with the words "in case of bad weather" on the invites?
That's exactly what you should do: Plan on an alternate location in case of bad weather (or plan to have an extra tent on hand at the outdoor site), then let your guests know. It's completely appropriate to include this information on your invitations. Some couples include a separate rain card enclosure with the invitation, which provides the 411 on what to do and where to go if in case of rain or snow.
Wedding Invitations + Wedding Stationery