While I don't mind standing under an umbrella in a soft rain (which can be romantic), your granny and your friend in the new 5 inch heels, and people who DID get dressed up for you may mind, a lot. Last night we had to move a wedding ceremony from the Music Garden, where the metal gazebo has no actual roof, to the reception site at the last minute. That meant the groom had to wait at the garden for all of those people who were still coming to the first site, even though the skies opened and it should have been obvious the rain wasn't going to stop.
Please have a "Plan B" - and a way to CONTACT your guests.
You will usually need to contact them BEFORE they set out for the wedding -- or it's going to be a logistical nightmare (in the rain) trying to get everyone to your other location. Appoint a contact person who is NOT in the wedding party, and give out their phone number to everyone. Post them at the original location to redirect - so the groom won't have to stay at the original site. Have a rain time already prepared, which is usually an hour later than the original wedding, so you have time to set up.
If you have the ability to simply move inside at the same location, talk to the site staff in enough time for them to adjust. We often have a ceremony area roughly set up in another room, and all you'll need to do is move chairs, or set up some chairs for family and older guests and have other guests stand at the back
Respect your guests - their clothes and shoes and hairdos - and respect your musicians - string players can't cope with rain, and they won't want their instruments to get wet. Electronics can't get wet - so ditch the DJ and let them go inside. In case of passing showers, you can always reasssemble outside for post-ceremony pix, toasts, and group pictures.