How would one go about doing this? Is it safe to freeze?
Pasta freezes well if you do it right. In fact, I know of a very famous Italian restaurant in NY that freezes their pasta which they make fresh everyday. They cycle through new pasta every three days and they serve A LOT of pasta. The chef dared me to tell the difference. And he's right. 99.9% of people can't tell.
To freeze, bundle into small amounts (e.g. wrap around your hand), enough for single servings. Put on a tray, with a little semolina flour or cornmeal dusted underneath (to prevent sticking). Keep each bunch separate, they shouldn't touch. Put into freezer. Once frozen (few hours), transfer to a ziplock freezer bag. It will keep for several months, but I'd eat it within one month.
To use, dump straight into boiling water. Make sure you have a big pot of water at a full boil (because the frozen pasta will drop the temperature more than unfrozen). Stir immediately.
This works very well.
Freeze away! After making the noodles but before cooking let the noodle air dry on a drying rack for maybe 30 minutes, then put in zipper freezer bags in whatever serving size you want. When it is time to eat - pull from freezer, have boiling salted water ready to go and plop it into the pan for 3-5 minutes. It will cook a lot faster. No need to defrost. You can also make raviolis and then freeze them. Works great for me, egg or egg-free.