I live in one of the coldest parts of the US, and for a house, 2x6 walls have become pretty much standard. For a detatched garage or other outbuilding, 2x6 still doesn't make much sense unless you need the additional structural strength. A 2x4 wall takes R13 fiberglass blankets, and you can add another R6 for the outside sheathing. That gives you a low priced R20 wall. A 2x6 built the same would be R26. When you are heating a building, you will never see any energy savings return between the two. A R20 wall coupled with a R50 ceiling holds all the heat you can economically contain. Your heat loss in a building like this is your doors and windows. You can't find R20 doors or windows. The windows if you choose double thermopane will be around R3. If you choose triple thermopane will be around R5. The doors will be significantly better than the windows, but nowhere near a good 2x4 wall.
And, all your air leaks will be at the doors and windows.
Simply said, UNLESS YOU NEED THE ADDITIONAL STRUTURAL STRENGTH, spending additional money on a 2x6 wall is money you will never see a return from in heating and cooling.