If using latex paint, your ambient temp is too low. Humidity too high, rain likely and conditions not inducive for this job.
Now, if you want to pay more and less coverage, seek out Sherwin' Low Temp latex paint. I have used it and its like Glidden paint if you will. Meaning its like whipped butter. I did not like the experience. Coverage per can drops considerably.
What I would do is to scrap the area well. Do not paint regardless until that wood had dried out or you will be doing this again at the same spot next Spring. Wet or damp wood will cause paint to peel and blister EVERY TIME.
I would wait till Spring on the complete job.
Please do not let a paint contractor tell you differently.