Take a needle and monofilament thread (fishing line) and attach a SMALL key ring to the back of the gloves, as close as possible to the gloves to where you can still access the ring with your carabiner. The ring makes for a good point to attach the gloves to your belt as you described (carabiner). I actually hook my heavier gloves to a belt loop in the same manner when on my tractor, then swap the thinner ones I use while driving the tractor out if I have need of the thick leather gloves I use for barbed wire, cattle panels, and rebar. I am really sick of stitching up my hands because of nearly bone deep cuts from handling metal without proper gloves, starting to think I was back in the Army putting out razor wire (with no gloves). Don't use a house size key ring, they will snag on stuff to easily, I mean small when I say small. The ring you want will hold roughly 2 to 3 keys max, it's just barely large enough for the carabiner to go through. I found mine at harbor freight. Get something other than chrome if available, no reflections. Also if the ring is dangling out the back of your gloves you did it wrong, dangling will catch on everything. You want to be able to (almost completely) hide the ring under the Velcro wrist strap when worn, if your gloves have one.
