An inch and a half goldfish should be TOTALLY fine to winter in a 15 gallon tank, especially if it is alone.
Keep up the good filtering and water changes and stop stressing yourself out worrying about it.
I have a 15 gallon with one medium sized gourami, 5 albino tiger barbs, a tiny algae eater or two and dozens of Malaysian trumpet snails. It runs with one aquaclear 20gallon filter. It is all but overrun with java fern varieties covering a huge chunk of driftwood and a bunch of less aggressively productive anubias plants chugging along on a smaller piece of wood.
I sometimes go two months without changing the water and every one is happy, very healthy and harmoniously getting along with their lives. Between the plants and the filter everything stays pretty clean; I do the water changes for the plants more than I do them for the fish any more. (Fresh water brings nutrients that the plants don't get from fish waste.)
The only thing I'd add to your 15 is some anubias plants tied down to river rocks or driftwood. It's one of the very few readily available plants that goldfish don't seem to like to nibble on. They're sturdy, they don't need much light, they add nice atmosphere, they're almost impossible to kill and they'll add some extra bio filtration to the system.
Your little fish will be fine. Winter isn't forever.