During winter time, land travel was difficult and sea travel practically impossible. To reach Corinth at the beginning of the winter would make good sense, since Paul wished to stay there for a while (1 Corinthians 16:7).
The words wherever I go
indicate that Paul is willing to use ministry opportunities as they present themselves. He is not set on reaching Jerusalem (or any other destination) as soon as possible, at the cost of other work which the Lord may have prepared for him.
Although Paul did not accept financial support from the Corinthians when he first preached the gospel to them (1 Corinthians 9:12), he will now welcome their help
on his further travels.
6 and perhaps I will stay with you or even spend the winter, so that you may help me on my journey, wherever I go.