Ah, it just struck me! What Mark just said about heating up the ground is true, but only in order to actually heat the hydrant, and I believe I know an easy way for you to do that!
Go to an auto parts store and get a heated dipstick. Basically, it will be a dipstick with an electric cord attached at the handle. Then, go to a hardware store and get a 3' piece of small angle iron, something like 1/2" x 1/2". Ask somebody at the hardware store to file the inside edges at one end of the angle iron so they will not gouge your riser pipe, then use a hammer to drive that angle iron vertically (and carefully) into the ground right next to your yard hydrant. Driving it into the ground only a couple of inches at a time, wobble it around a little and pull it up and start over several times so you do not end up getting it stuck in hard ground. At some point after you have gone into the ground at least a foot or so, set the angle iron aside and place the heated dipstick in the ground and right next to your riser ... then wrap the two together with something that will not easily melt and put your insulation back around it for a while. That dipstick is going to get much warmer than heat tape, and maybe you can even push it down a little more as the ground begins to soften.