You need to follow below steps to save custom field value.
Below code will be work for both the login and guest user. Also please create field in "quote_address" and "sales_order_address" table first. Here i have shown you code according to the field "customtype". Please change field according to yours.
Step 1:- Create file ...
Please follow the below blog
this is helpfull for you to refresh shipping rate when change zipcode and country