Including javascript globally using webpack - vue.js

Question

I'm using webpack and Vuejs. I have several components in my application, and I want to use momentjs globally. Everything I've tried so far doesn't seem to work and throws and Undefined error in console. Is there a way to get set moment.js globally available to all components from main.js using webpack?
These are the things I've tried (in main.js):
import moment from 'moment';
Vue.prototype.$moment = moment;
In a component I try to access it via this.$moment but get an undefined error.
I also tried:
import moment from 'moment';
Object.definePrototype(Vue.prototype, '$moment', { value: moment });
I also tried to access it via this.$moment, but get the same undefined error on this.$moment.
Am I missing a step or doing something wrong to include a javascript file globally to all components using webpack?
Thanks again for the help!
UPDATES
By the way, momentjs works fine if I import it in every component I want to use it in (as follows, however, this is what I'm trying to avoid):
import moment from 'moment';
...
let today_date = moment().format('YYYY-MM-DD');
UPDATES 2*
This is the exact error (with using this.):
Error in render function: "TypeError: Cannot read property '$moment' of undefined"
This is error (without using this.):
Error in render function: "ReferenceError: $moment is not defined"
Moment is added via dependencies in package.json:
...
"babel-plugin-syntax-dynamic-import": "^6.18.0",
"babel-plugin-transform-class-properties": "^6.24.1",
"babel-plugin-transform-runtime": "^6.23.0",
"babel-preset-env": "^1.6.0",
"css-loader": "^0.28.5",
"es6-promise": "^4.1.1",
"moment": "^2.18.1",
...
Code usage within a component:
...
filters: {
getYear(date) {
return this.$moment(date).format('YYYY');
},
getMonth(date) {
return this.$moment(date).format('MMM');
},
getDay(date) {
return this.$moment(date).format('D');
},
},
...