Loop through multidimensional list and add value of its one field to a string List., I get variable does not exist error

Question

Here I am pulling in data in bulk using the below statement

List<sumchans__MDU_Squad_Raw_Data__c> addressData = [SELECT sumchans__Street_Address__c,sumchans__City_Name__c,sumchans__Province_Code__c,sumchans__Postal_Code__c
FROM sumchans__MDU_Squad_Raw_Data__c WHERE sumchans__Street_Address__c IN :streetList AND sumchans__City_Name__c IN :cityList];

Using a for loop traversing through the addressData list above I am creating an addressMaster List below:

    List<sumchans__Address_Master__c> addressMaster = new List<sumchans__Address_Master__c>();
    for(sumchans__MDU_Squad_Raw_Data__c raw : addressData) { 
          String fullAddress = raw.sumchans__Street_Address__c+' '+raw.sumchans__City_Name__c+' '+raw.sumchans__Province_Code__c+' '+raw.sumchans__Postal_Code__c;      
          sumchans__Address_Master__c address = new sumchans__Address_Master__c();
          address.Full_Address_Ext_Id__c = fullAddress;
    }
addressMaster.add(address);

Now I am looping through the addressMaster list and adding the value of the Full_Address_Ext_Id field to a String List, for some reason I get an error saying variable does not exist. Not getting what I am doing wrong here. I have added everything to the addressMaster before accessing it below.

List<String> addresses = new List<String>();
for(String fullAddress: addressMaster) {
    addresses.add(fullAddress.Full_Address_Ext_Id__c);// This statement says variable does not exist.
}
List <sumchans__Address_ColdCustomers__c> deletePrevColdCustomerList = [Select Id from sumchans__Address_ColdCustomers__c where Name in :addresses];
Delete deletePrevColdCustomerList;

EDIT after applying David Reeds answer

List<sumchans__Address_Master__c> addressMaster = new List<sumchans__Address_Master__c>();
for(sumchans__MDU_Squad_Raw_Data__c raw : addressData) { 
      String fullAddress = raw.sumchans__Street_Address__c+' '+raw.sumchans__City_Name__c+' '+raw.sumchans__Province_Code__c+' '+raw.sumchans__Postal_Code__c;      
      sumchans__Address_Master__c address = new sumchans__Address_Master__c();
      address.sumchans__Full_Address_Ext_Id__c = fullAddress;
}

addressMaster.add(address);

Is this the way you mentioned:

List<sumchans__Address_Master__c> addresses = new List<sumchans__Address_Master__c>();
for(String fullAddress: addressMaster) {
    addresses.add(fullAddress.sumchans__Full_Address_Ext_Id__c);
}
List <sumchans__Address_ColdCustomers__c> deletePrevColdCustomerList = [Select Id from sumchans__Address_ColdCustomers__c where Name in :addresses];
Delete deletePrevColdCustomerList;

Answer 1

There's likely two problems here.

for(String fullAddress: addressMaster) {

addressMaster is typed as a List<sumchans__Address_Master__c>, not a List<String>, so your loop variable is the wrong type.

But also, you're referring to this field without a namespace prefix in two places:

      address.Full_Address_Ext_Id__c = fullAddress;
addresses.add(fullAddress.Full_Address_Ext_Id__c);

If that field is part of the managed package, as opposed to an unpackaged custom field, you need the sumchans__ prefix.