I presume that these pictures you posted here were taken with the 60mm then? Just curious, how did you go about taking these shots? From the shutter speed used, I can tell that they certainly weren’t hand-held! Did you use a tripod?
In regards to getting better results, you might try “opening up” to f/8-f/11 or so. According to Ken Rockwell, the diffraction limited aperture of the Nikon 60mm Micro is f/11. (Note: That is for the AF-S version, but I would guess it’s about the same for the AF-D)
If you have the AF-D version, an inexpensive way to get more magnification is to use extension tubes. Note that if you own the AF-S lens, you’ll lose all electronic functions, AF, and aperture control. I think you can buy extension tubes which will let you keep the electrical connections, but they are quite expensive, and as I’ve never used Nikon, I don’t have any idea how well they work. I think your best option is a 60mm AF-D with extension tubes, and if that’s not enough, buy a cheap 28mm lens and reverse it on the end of that! An 18-55 kit lens probably won’t work very well, because you can’t control the aperture, but don’t let me discourage you; do some experimenting and prove me wrong!
I was just testing out some “new” lenses recently. I used some pollen from an Easter lily and some table salt to test for sharpness, magnification, etc. If you take a glass casserole dish and invert it on a table, you can shine a light up through it and use that for testing your setup. Just put a few grains of salt/sugar on the glass, and see what you can come up with! I attached a few pictures that I got the other day, just for your inspiration. As near as I can calculate, both of those pictures have ~7:1 magnification. The first one is a grain of raw sugar, the second is pollen from an Easter lily. The image of the sugar is uncropped, so it actually does almost fill the frame!
I personally use a combination of extension tubes, prime lenses, and reversed lenses! Here’s a picture of my setup on Google+. There are several examples of snowflake photos taken with that setup here on Lenspiration, and there are many more on my Google+ account.
Keep trying! You’re already doing a lot better than I did when I first started taking snowflake pictures! Here is one of my very earliest attempts…
As you can see, I forgot to turn down the ISO, I think it was at ISO 800, which is way too high for a little point-and-shoot camera.