I then made some coffee-flavored ice cream which could easily be turned into a Frappacino (just let it melt for a few minutes).
Here's what I'd suggest:
In a bowl, mix coffee the way you like it and add some milk. You can play around with this. I added some 1% milk in addition to the usual amount of flavored creamer. I suggest that if you use sugar, you add a bit more than you usually would with your coffee. If you want it sweeter, stick closer to the amount of sugar called for in the snow ice cream recipe (With liquid Stevia, I found the usual amount I used in my coffee worked, but with sugar, sticking closer to the snow ice cream amount worked well).
Mix it all together first in the bowl. I added bits individually and it didn't blend well. So mix coffee, sugar/sweetener (artificial sweeteners may not lend themselves well to this), creamer and milk together. Then get fresh snow and add and mix little bits at a time. You'll probably find you can add much more snow then you originally thought. For snow ice cream, we used two large sized pitchers full of snow. For my Frap, though, I used 1 and 1/4 pitchers. It depends on how much liquid you use.
Put it in a cup and depending on whether you have absolutely no patience or if you can wait a few minutes, you'll either have coffee-flavored snow ice cream or a super cheap Frappacino (for a fraction of the WW points that are in the Starbuck's version--a grande no whip Mocha Frappachino is 5 points. Mine came out to less than 1 point per serving when I used Stevia in place of sugar).