I'd be suspicious about that apple tree being self-pollinating. There may be some varieties that are, and maybe you know something about that specific tree, but self-pollinating apples are pretty rare. If there is another apple tree within the area, even a crabapple, you should be OK, but even a lot of self-pollinating trees do much better if there is a different variety near by.
One option you might consider is to get those trees where two or more varieties are grafted onto one tree. That way you solve the one tree per variety issue. You also get better production from cross-pollination, even if it is not absolutely required. I have one Asian pear tree that has two varieties grafted on one rootstock. That works well for me here, but I occasionally have nights below 0* F. You're probably not cold enough for Asian pear.
I'm having trouble coming up with trees that might do well in that climate if you only get in the low 20's occasionally. That sounds similar to the Gulf Coast and there are not a lot of fruit trees that do well there. I'm going by what you said was occasional low 20's instead of the zone since I'm confused about that. Many fruits require a certain number of cold days or cold hours to do well or even produce at all. Citrus may be your best option, but there are risks with that. You might talk to your county extension agent, in the phone book under county government, and see what they recommend for your area. Or try to get hold of a master gardener and ask them. You can also try talking to people at a tree nursery. I'm not talking about Home Depot or Lowe's, but an actual nursery run by people that know about your local climate, not somebody selling through a chain. You might get lucky, but those are not always as "local" as you might need.
I had a lime tree when I lived in the New Orleans area. We'd maybe barely have a freeze once or twice a year most years, but several years they would be so light I'd have tomatoes or peppers live though the winter without protecting them. A real mild climate. Even if I covered it when we had a freeze, the line tree would sometimes die back and regrow from the roots. A neighbor had a lemon tree that did the same thing. Since these were grafted trees, what grew back was from the rootstock, not the grafted part. That was OK by us, although we lost a few years of production while it grew back to production size. The fruit produced by the rootstock was not as pretty as the grafted variety, but it was big, thin-skinned, and really juicy. For my purposes, which was cooking, it did not have to be pretty. I was not trying to sell it.
But my point is, if you try something and it freezes out, what comes back from the rootstock will not be the same as the grafted variety. I'd be real careful of things that can't take the cold, like citrus. If you only occasionally get those temperatures, like once every several years, you might get some production from a citrus, but you might lose it when you get those cold winters and you don't know what will come back from the rootstock. Location matters too. You get more frost in low valleys than on hillsides or on top of a hill. Cold air will settle on a calm night.