I got another idea, I so this once but completely forgot about it. Instead of this;
<input type="number" id="codice_prodotto" name="codice_prodotto" ng-model="codice_prodotto">
use this:
<input type="number" id="codice_prodotto" name="codice_prodotto" ng-model="codice_prodotto.value">
And in your controller:
console.log($scope.codice_prodotto.value);
###EDIT
You need to use dot notation with Ionic and input elements placed inside a ion-content container: