It doesn't look like it has any roots. I've repotted mine a few times and it has a massive root system for such a "small" tree. I never let the soil get completely dry. A recent pic.

Can you put it with its pot into the tank? It's worth trying. I would put it in the pot, cover the little roots up, give it a good thorough watering, let it drain, and give it a try. Keep in mind ponytail palms are succulents so don't over water it and make sure it's not too humid in the tank. It might need some airflow.

I would place it in a sunny window until spring. Ponytail palms don't actively grow during the winter. Their trunks are designed to store the water they need, so I don't water mine a whole lot this time of year. But they can still photosynthesize the the energy they need and store it up until when they need it later on. When spring rolls around, they will start sending out new growth. Which is why I would just keep them in a sunny window. Your ponytail palm will be just fine until then. Let it soak up that sunshine in the meantime. I wouldn't try forcing it to start growing any sooner than it will on its own. You can repot it now with some fresh, fast draining soil, or wait until spring. They're not picky about that.