Answers

It depends on how much storage you need, how you access it, available space between joints and ground and is area conditioned? Do you have some pictures and rough dimensions?

I have constructed wine cellars and installed basements under existing houses. I can tell you right up front it won't be cheap. And it is not easy.

Have you considered building an above ground wine cellar, or building one underground but not under the house?

If you have standup space below grade near the kitchen and a dry foot print beneath your home you may want to consider consulting with a designer or builder to explore the possabilities. Often  it is necessary to dig out and incorporate masonry and / or stone work into the restraining walls and floor. The objective of the cellar is to create an environment maintain a constant temperature and humidity.

Needless to say, depending on size a cellar will allow you to stock pile volume and will give you an opportunity to age choice ventages yourself. Good luck!