Painted water base paint over oil base paint on wood not drying

These days water based exterior paints are as good as oil and some will last longer (Zinsser Allcoat exterior for example and that will go on top of oil gloss with no problem). However, in this case I would suggest it's because you are painting outside when the temperature still drops significantly during the night and the paint wont dry properly. Your best bet would be to leave it for a few days and see if it dries off any better now that the nights are a little warmer. You are taking a chance in not sanding the old paint though so even when the new paint is dry you might have issues. Anyway, if the new paint dries in a few days you can try gently sanding and then do another coat.

stay with oil base in all cases outside, wipe down all areas , sand down when dry and apply 2 coats of oil base paint. oil base will more than triple the life span of any water base exterior paints.

Always use oil paints for outside will last a lot longer than water based paints and a lot harder wearing for outside work

First problem is you didnt sand it. It takes times and a bit of care in the preperation to get it to adhere properly. Ideal would be to use Acrylic based paint drys quick and tough . Oil basedis fine if you can leave between coats No dust around and clean surfaces. Hoover all dust when sanded and check for flaking.