Water dripping through roof of covered patio in several places-lots of snow on roof- not leaking into house just patio.

What is your question?

Your covered patio obviously has a leak that will have to be repaired once warmer weather sets in. Right now you can't do anythng except take and mark where the water is leaking in so you'll have an idea where to start looking for the water intrusion in the spring.

Also, your house roof needs to be inspected thoroughly in the spring to be sure there are no leaks in that either.

Do you have the porch properly pitched so that the melting snow water can be properly diverted away down the gutters and away from the foundation of the porch? That might be your problem - an improper pitch to your porch roof.