Can this thermostat be detached from the mat and used with larger heating mats?
Yes, the thermostat can be detached.
Can you use this to keep an animal warm?
Sure. You can set it for whatever temp you want (within a certain range). Might want to put a blanket between the animal and the mat. It works great, keeping the box at a near constant 70 degrees.
Can I heat and keep my wine warm?
Yes. As long as you set the temperature you want, you can make the heating pad work. It can even ferment your bread, and can be used to raise snake boxes, and chick coops.