Could these be glazed? I guess it would have to be a pretty thin glaze as not to deflate the dough. What you do think?

Hi Sarah! You can definitely glaze the doughnuts after they're fried. Here's a great resource by Erin McDowell with lots of ideas for glazes: https://food52.com/recipes/28778-basic-yeast-doughnuts-with-many-variations