What wine fridge are you buying? Where is the kitchen/pantry layout? A good wine fridge is temperature controlled, even dual temperature in many instances. In any scenario, in any climate, the shared exterior wall /garage is insulated as are all other exterior walls. Show the plan. The pantry shouldn't vary in temperature very far from the temperature in your kitchen

Yes. You should run HVAC to the new finished pantry space. You will also need an HVAC return in the pantry. These will keep down the growth of mold and mildew. You will want this even if you weren't adding any appliance to this new space.

Your appliance will produce heat and the pantry will be very warm if you don't put in HVAC. I did this myself by enclosing some area of the porch. The appliance I put in the area really produced a lot of heat.

I assume that your unit is freestanding or will be enclosed in cabinetry. You will need nothing else. However, make sure the finished space is insulated as if it were part of the conditioned space of the home. If you are carving this space out of a garage, you will need to be certain that it is built with firewall from the garage and that it does not share ventilation from the garage. This project will need a building permit in most parts of the country, there are always exceptions.

You not only need climate control, electrical, correct foundation, vapor barrier, sill seal barrier, and all the other requirements of habitable space construction, but you also need to maintain the fire wall between the garage and home, and with no penetrations into it. If you are doing a door into the garage from the pantry, it has to be fire rated.