A suitable post hole depth for a 4′ fence

Assuming that you plan to set the posts in concrete then you should follow these rules:

For wind strength:

The post should be buried 33%-50% of the exposed height

You'll be exposing 4 feet above ground so the buried portion should be 1.3-2 feet; your 6 foot post will suffice for wind strength especially since a picket fence has large gaps between the vertical boards.

For frost protection:

You're in zone 6 so the bottom of your post should be at least 30 inches below the ground.

You plan to use 5 inches of gravel? You need to dig down 35 inches.

Do not skimp on protecting against frost!

When water freezes, it expands about 9 percent—think of how ice cubes are domed above the original water level in the ice cube tray. Ice exerts a pressure of about 50,000 lbs. per square inch—enough force to lift even a large building. A puny little deck on inadequate footings doesn’t stand a chance.

The reason buildings and decks don’t always return to their original height is that surrounding dirt sometimes fills in under the footing while it’s lifted.

Heavy clay soils don’t drain well, so they tend to have more frost heave problems than sandy, well-drained ones. But even if footings are deep enough, ice lenses can latch onto the rough surfaces of wood and concrete and lift footings and posts from the side. That’s why concrete piers poured in waxed cardboard tubes and smooth wooden installing deck posts work well for below-grade support.

https://www.familyhandyman.com/project/how-to-build-a-solid-frostproof-deck-footing/

In conclusion:

1. Dig down 35 inches
   • The hole width should be at least 3x the width of your post; 4x3 = 12" wide hole
2. Place your 5 inches of gravel
3. Pour 6 inches of concrete
   • Place 6 inches of solid material such as a brick into the center of the concrete to make step #4 possible
4. Place your post on top; 2 feet below the ground should leave you with 4 feet above ground
   • You may find that it's easier to just set taller posts and cut them down short later since land is almost never perfectly straight. Some posts might be 4 feet above ground and others might be 5 feet.
5. Pour 2 feet of concrete around your post
   • Use a post level to make sure everything is perfectly vertical
   • See https://diy.stackexchange.com/a/226599/42053 for how to use braces if you want perfection
6. Pour extra concrete so that it rests an inch or two above the dirt so that you can slope it outwards to prevent water pooling near the wood