Since no one has posted an answer, I'll turn my comment into one, even though it is not going to give you a quantitative answer.
The reason that I can't give you a number is because the answer is simply, "lots." Any crater that is on the north or south polar layered deposits (N/SPLD) are going to have permanent ice in them, by definition, since they formed in ice. Since the NPLD is much younger than the SPLD, it has many fewer craters.
The largest (off the top of my head) on the SPLD is McMurdo, roughly 30 km across. Korolev is larger at about 81 km across, but it is not on the NPLD. Korolev itself is large enough that it has its own mini-climate with positive feedback mechanisms to keep the ice there, but smaller craters can't do that.
To get permanent ice in craters not in the N/SPLD, you need to keep the temperatures cold enough and pressure high enough for the ice to remain throughout that hemisphere's summer. Since the northern hemisphere's summer is when Mars is near aphelion, getting 45% less sunlight than during southern summer, craters can be closer to the equator and still meet that requirement. Also, the northern hemisphere is lower in elevation than the southern, so you also get more atmospheric pressure which helps keep the ice from sublimating. You're also going to want a high enough rim and/or deep enough crater cavity to guard against sunlight as much as possible, so larger craters (like Korolev) are again going to be preferable to small ones. But, Korolev is the largest crater closest to the NPLD, so that's why it's be best known for this sort of phenomenon.
So, are there others? Certainly. But, they're smaller. And, unless an impact crater is scientifically important and has had a name nominated for it through the International Astronomical Union, it is not going to be named, so very few craters on Mars are named.
To answer your question about which is the closest to the equator, it is not something I'm sure has ever really been looked at. One would need good, repeat mosaics at different points in Mars' orbit and simply do a visual search. If you do do that, happy hunting!