Not as hard as you might think. Built a sub-zero freezer that held tractor trailer loads of ice for about a third of what the commercial variety sold for.
Cold wants to travel down and moisture moves toward dry, so you have an insulation challenge and a vapor migration issue to resolve. Also heat transfer flows like water in that it takes the path of least resistance.
All of that means that you ideally want as uniform an insulated envelope as possible, with your vapor barrier as close to conditioned space as possible. . With an existing structure this is easiest done with iso-foam board available at any home center, but companies like Insulation Depot, et al, often have perfectly functional recycled available for less than half the cost of new. It can be glued right to an existing wall finish. Get the stuff with foil on one side (and install it with the foil face out) as this also acts as a radiant barrier, keeping the long wave radiation (heat) from the sun that penetrates most homes' walls with ease, from getting through. "R" values per inch of this is about "10", so it's extremely efficient, whereas fiberglass by comparison is a complete waste of money. EPS (Styrofoam) is usually used for floors since it's more stable when a load is placed on it, but it's nowhere near as efficient - requiring almost twice as much bulk per inch, so we came up with a way to get around that. BTW, when working with the foam board, be sure to seal and cut everythin as tight as possible. You can use the canned spray foam to fill any gaps, but also cover all seams with good quality foil tape (3M or Scotch, not the Chi-Com crap). Also make sure any wall penetrations are sealed with spray foam and caulk. Our doors were triple layered thin wood frames with the same kind of finishes, vinyl strip barriers, and a stepped jamb with multiple layers of silicone bulb weather stripping. The door took some effort to close against all of the weatherstripping, but it also never leaked.
First screwed 2"x2" treated stringers on the floor at 12" on center and filled between them with 1-1/2" thick panels of the iso foam board. Then we laid another layer of 1-1/2" treated stringers at a right angle across this and filled between them as well. What this accomplished was that except for the 1-1/2"x1-1/2" squares where the two stringer layers crossed, we had a pretty uniform layer of insulation. Where they crossed the "R" value was only "3" since wood has an "R" value of about "1" per inch of thickness. To help mitigate that condition we added two more layers that were offset 6" from the first two and covered that with two layers of glued and screwed tongue and groove 3/4" OSB. Ultimately we had a floor that sat about 7-1/2" higher than the surrounding room and had an "R" value of about "60". We ran electric pallet jacks loaded with 2,800 lb. pallets of ice over this for a year before we could afford to cover it with diamond plate and it held fine. Obviously a beer closet won't require near that level of support, so maybe three layers of stringers with a single layer of OSB covering would do fine (R-45 +/-). Use the same thickness on the walls and ceiling, cover them with just 7/16" OSB and paint the floor, walls, and ceiling with a vapor barrier primer (Kilz & Zinzer both make one). It dries fast (like 15 minute between coats) but the fumes are deadly, so use a half mask respirator AND plenty of ventilation when nobody is home for the day. Then you can coat with epoxy on the floor and FRP (Fiberglass Resin Panels, available at the home stores) on the walls for durability and cleanability, or check out some of the new acrylic coatings that are sold for resurfacing decks and such (Roll Stone, etc.).
Used the same approach to build a cheap cooler for our fruits and vegetables as they come out of the field and a little 15,000 btu unit keeps everybody happy with a little thermostat trickery.
Instead of chopping a hole in the wall you might also look at using one of the roll around a/c units. I recently bought a dozen from a local discounter for $5 a piece that were returns. They're in the liquidation end of retail so they don't do RTV's on returns and damaged goods, they just mark them out and toss them in the compactor. I have a deal where I have to take everything but usually most of the stuff works just fine. People buy it for a really hot week and then return it for the money. Sucks for the retailer but I get all kinds of great deals on stuff that would otherwise go to the landfill. Even the remanufactured ones are cheap enough. The roll arounds use a big flex hose for their discharge, and a piece of PVC or tubing is best installed to get the condensate outside, but that way you only have a 6" vent pipe and a small piece of tubing that you have to route through the wall. The vent could go up and tie to an existing exhaust fan duct if the size is adequate. Just don't vent to your attic or eaves as the moisture laden exhaust WILL wreak havoc (mold insulation and rotten eaves & facia boards).
Some of the newer roll arounds are actually mini heat pumps that can cycle either way, so there's also added flexibility potential with that.
