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.