From IMBA's rules for mt. bikes:
"Be sensitive to the dirt beneath you. Wet and muddy trails are more vulnerable to damage than dry ones. When the trail is soft, consider other riding options. This also means staying on existing trails and not creating new ones.."
From BCH and California State Horsemen:
Avoid sensitive areas and wet or muddy trails. Leave no Trace. Practice Gentle Use Principles. Be sensitive to the earth beneath you. Recognize different types of soils and trail conditions. Wet and muddy trails are more vulnerable to damage, so consider other options. Please stay on existing trails; do not create new ones and do not shortcut."
So, where do you ride?
First, wait. Wait for 24 to 48 hours after the last rain for most trails to adequately dry out. If there are puddles in the middle of the trail, DO NOT RIDE AROUND THEM. Your horse or bike will widen the trail - soon, instead of a 5 feet wide trail, you have a 15 feet wide trail of ruts.
Where is the best place to ride after I wait?
The sandier, the better. Sandy soil drains much faster than clay soil. In our area, for example, the trails around Folsom Lake SRA have a natural base of decomposed granite and are good to go after the wait. Or, stay on the gravel ranch roads at Hidden Falls Regional Park or Empire Mine.
Where shouldn't I ride right after the rains?
Trails that are clay based will retain water longer, your tires and hooves will slip and slide, destroying the trails. Typical red clay-based trails are the narrow, cliff side trails in Hidden Falls Regional Park.
On these rainy days, it's a good time to repair and clean your bike, brush your horse, and wait for the sun to dry out the trails. Or put on your hiking boots and enjoy walking the quiet trails.