2002 Oldsmobile Alero Catalyst converter

I HAd my car checked for trouble beacuse my check engine light came on , so they told me that i needed a catalyst converter. At first my car was driving fine now that its colder outside i notice my car missing from the tail pipe, it acts like it wants to shut down and i sometimes can smell exaust fumes . Are these symptoms from a faulty catalyst converter if not can you explain to me what to exspect knowing that i have a faulty cat converter can it stop my car from running or can i damage anything driving it during these times.