The minimum focus distance is indeed the minimum distance you'll need to take (from sensor to subject) to be able to focus. The lens can't focus closer than that. A way to get around this is with an extension tube which lets you move the lens closer to the subject and increases magnification at the cost of some light.

If the ice is stable and you have the camera firmly mounted you can go with slow shutter speeds, possibly slower than 1/30. If that helps to use a narrower aperture (higher f-stop) then you could increase the depth of field that way. You can also try to reduce vibrations by using a remote shutter button and the mirror lockup function if the camera has it.

Even with all that, macro shots can have very, very thin depths of field. A flat-looking ice crystal might still have too much relief to get everything as sharp as you want. At that point it's interesting to look into the technique of focus stacking. This means taking multiple pictures at different focus distances (although still very tiny differences in absolute terms) and then having parts of those pictures combined to get one image with substantially more in focus. Your subject has the advantage of not suddenly flying away or moving around like with plants or animals, which can make the technique easier to apply.