If I start community college in the winter semester do I still have a chance to transfer to a university?

It doesn't matter when you start, if you finished your associate's degree in, say, December, you might not be able to start as a junior at a university until the following fall. It would depend on whether the university admitted for semesters or quarters other than fall. Some allow that, some don't.

The university will not care when you started CC. Once you earn 30-45 credit hours at the CC, apply to transfer over to the U.

Are you asking if you could transfer for next fall? You'd have to contact the university to find out when they cut off transfer applications. You probably would not have any grades or transcripts to send yet.

You might if you take summer school...