First thing to know is what model of Rolleiflex because this winding problem I have seen it in models T and GX/FX.
Transport is quite different with previous models from A to F, if you and unsure what model you have, check this link:
Chonological overview of all 6x6 Rollei Rolleiflex TLR cameras
rolleiclub.com
Now the issues, shutter and transport. They are linked in the way one allows the other to work when each one finishes its action, but no much more.
Is film spacing ok?
You are saying lately, same results when you try outside (winter=cold=old grease slows down everything) than inside? I have seen problems from 5 C degrees and below.
I might be completely wrong and the issue is related to something else, only opening one can tell. Best solution take it to a repair tech in your area.