Add warm water and yeast in a bowl and wait 2 minutes.
Add eggs and vegetable oil to mixture and blend.
Pour in apple cider.
In another bowl, add cinnamon, salt, sugar and flour and sift together.
Add to liquid mixture, adding more flour if dough is too wet or sticky.
Knead for 5 minutes or until dough is elastic and worked through.
Cover bowl and let rise for 30 minutes.
Roll out dough to about 3/4 inch thickness and cut out doughnuts.
Place on a piece of parchment paper and let rise in a warm place for 45 minutes.
For frying: Heat oil up to 375 and fry doughnuts for roughly 30 seconds on each side or until they are golden brown.
Remove from oil and place on a cooling rack or paper towel.
For baking: Preheat oven to 350 Bake for 13-15 minutes or until they are cooked through.
Whisk together the butter, cream cheese, vanilla, powdered sugar, milk, apple cider, cinnamon and nutmeg and blend until smooth.
Dip each doughnut in the glaze. Enjoy!