Can I have a4 foot pool without a fence

This type of law is a municipal ordinance and it's different in each town. You have to contact the zoning department in your town to find out.

I would not chance it with kids around. Kids will be drawn to this attractive nuisance and there could be an unfortunate accident. In an abundance of caution I would definitely get a fence erected.

Even if the city does not have a rule, every insurance company I know of, requires a fense around the pool before they would insure you.
** unless it is an above ground pool where you can remove the ladder.