Just got an alignment a week ago, but now I need some snow tires. Would I need to get it done again or should I be fine?

 

You will be fine.

The reason why people usually recommend an alignment when you get new tires (or wheels and tires) is because people usually don't get alignments done regularly, so it's better for the life of the new tires you just spent a lot of money on...

 

just get the wheels balanced. It's not necessary to get wheel alignment.