Xbox Live Silver is enough to buy and download DLC and other items from the Xbox Live Marketplace. This page on the Xbox website explains the additional benefits of Gold membership.
Although that page's summary of Xbox Live Silver doesn't explicitly mention DLC, I can confirm that it is possible to purchase DLC (like Season Pass content is) with only Xbox Live Silver.
Do note that if the Season Pass comes with content that is multiplayer-only (such as new maps for a competitive multiplayer game), you may need Gold in order to fully utilize it. For instance, if you bought a Halo 4 season pass with Silver, you could download the new multiplayer maps and use them in LAN or split-screen, but not actually play them versus other people on the internet without shelling out for Gold.